"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# correlation\n",
"correlation = dataset.corr()\n",
"plt.figure(figsize=(15,15))\n",
"plt.title('Correlation Matrix')\n",
"sns.heatmap(correlation, vmax=1, square=True,annot=True,cmap='cubehelix')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As it can be seen by the picture above there is a significant positive correlation between the stocks. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## 4. Data Preparation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## 4.1. Data Cleaning\n",
"We check for the NAs in the data, either drop them or\n",
"fill them with the mean of the column and the steps are same as mentioned in previ‐\n",
"ous case studies."
]
},
{
"cell_type": "code",
"execution_count": 167,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Null Values = True\n"
]
}
],
"source": [
"#Checking for any null values and removing the null values'''\n",
"print('Null Values =',dataset.isnull().values.any())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Given that there are null values drop the rown contianing the null values."
]
},
{
"cell_type": "code",
"execution_count": 168,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
\n",
"\n",
"
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" \n",
"
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"
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"
TRESY1mo
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"
TRESY3mo
\n",
"
TRESY6mo
\n",
"
TRESY1y
\n",
"
TRESY2y
\n",
"
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\n",
"
TRESY5y
\n",
"
TRESY7y
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"
TRESY10y
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"
TRESY20y
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"
TRESY30y
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"
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"
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"
Date
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"
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"
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"
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"
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"
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"
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" \n",
" \n",
"
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"
2001-07-31
\n",
"
3.67
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"
3.54
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"
3.47
\n",
"
3.53
\n",
"
3.79
\n",
"
4.06
\n",
"
4.57
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"
4.86
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"
5.07
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"
5.61
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"
5.51
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"
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"
\n",
"
2001-08-01
\n",
"
3.65
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"
3.53
\n",
"
3.47
\n",
"
3.56
\n",
"
3.83
\n",
"
4.09
\n",
"
4.62
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"
4.90
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"
5.11
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"
5.63
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"
5.53
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"
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" \n",
"
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"
"
],
"text/plain": [
" TRESY1mo TRESY3mo TRESY6mo TRESY1y TRESY2y TRESY3y TRESY5y TRESY7y TRESY10y \\\n",
"Date \n",
"2001-07-31 3.67 3.54 3.47 3.53 3.79 4.06 4.57 4.86 5.07 \n",
"2001-08-01 3.65 3.53 3.47 3.56 3.83 4.09 4.62 4.90 5.11 \n",
"\n",
" TRESY20y TRESY30y \n",
"Date \n",
"2001-07-31 5.61 5.51 \n",
"2001-08-01 5.63 5.53 "
]
},
"execution_count": 168,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Fill the missing values with the last value available in the dataset. \n",
"dataset=dataset.fillna(method='ffill')\n",
"\n",
"# Drop the rows containing NA\n",
"dataset= dataset.dropna(axis=0)\n",
"# Fill na with 0\n",
"#dataset.fillna('0')\n",
"\n",
"dataset.head(2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## 4.2. Data Transformation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"All the variables should be on the same scale before applying PCA, otherwise a feature with large values will dominate the result. We use StandardScaler in sklearn to standardize the dataset’s features onto unit scale (mean = 0 and variance = 1)."
]
},
{
"cell_type": "code",
"execution_count": 169,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rescaledDataset.plot(figsize=(14,10))\n",
"plt.ylabel(\"Rate\")\n",
"plt.legend(bbox_to_anchor=(1.01, 0.9), loc=2)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"# 5. Evaluate Algorithms and Models"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## 5.2. Model Evaluation- Applying Principle Component Analysis"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As the next step We create a function to compute Principle Component Analysis from Sklearn. This function computes an inversed elbow chart that shows the amount of principle components and how many of them explain the variance treshold."
]
},
{
"cell_type": "code",
"execution_count": 171,
"metadata": {},
"outputs": [],
"source": [
"pca = PCA()\n",
"PrincipalComponent=pca.fit(rescaledDataset)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## 5.2.1.Explained Variance using PCA"
]
},
{
"cell_type": "code",
"execution_count": 172,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
Explained Variance_Top 5
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"
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"
0
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"
84.36%
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"
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"
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"
1
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"
98.44%
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"
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"
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"
2
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"
99.53%
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"
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"
\n",
"
3
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"
99.83%
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"
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"
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"
4
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"
99.94%
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"
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"
"
],
"text/plain": [
""
]
},
"execution_count": 172,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"NumEigenvalues=5\n",
"fig, axes = plt.subplots(ncols=2, figsize=(14,4))\n",
"pd.Series(pca.explained_variance_ratio_[:NumEigenvalues]).sort_values().plot.barh(title='Explained Variance Ratio by Top Factors',ax=axes[0]);\n",
"pd.Series(pca.explained_variance_ratio_[:NumEigenvalues]).cumsum().plot(ylim=(0,1),ax=axes[1], title='Cumulative Explained Variance');\n",
"\n",
"# explained_variance\n",
"pd.Series(np.cumsum(pca.explained_variance_ratio_)).to_frame('Explained Variance_Top 5').head(NumEigenvalues).style.format('{:,.2%}'.format)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Indeed, the first principal component accounts for 84.4% of variance, with the second principal component getting 98.44% and the third 99.53%. The first 3 principal components account for, cumulatively, 99.5% of all movements in the data. Hence, in terms of dimensionality reduction, the first 3 principal components are representative of the data."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## 5.2.2. Intuition Behind the Principal Components"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We\n",
"first have a function to determine the weights of each principal component. We then\n",
"perform the visualization of the principal components."
]
},
{
"cell_type": "code",
"execution_count": 173,
"metadata": {},
"outputs": [],
"source": [
"def PCWeights():\n",
" '''\n",
" Principal Components (PC) weights for each 28 PCs\n",
" '''\n",
" weights = pd.DataFrame()\n",
"\n",
" for i in range(len(pca.components_)):\n",
" weights[\"weights_{}\".format(i)] = pca.components_[i] / sum(pca.components_[i])\n",
"\n",
" weights = weights.values.T\n",
" return weights\n",
"\n",
"weights=PCWeights()"
]
},
{
"cell_type": "code",
"execution_count": 174,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"weights = PCWeights()\n",
"NumComponents=3 \n",
" \n",
"topPortfolios = pd.DataFrame(weights[:NumComponents], columns=dataset.columns)\n",
"topPortfolios.index = [f'Principal Component {i}' for i in range(1, NumComponents+1)]\n",
"\n",
"axes = topPortfolios.T.plot.bar(subplots=True, legend=False,figsize=(14,10))\n",
"plt.subplots_adjust(hspace=0.35)\n",
"axes[0].set_ylim(0, .2);"
]
},
{
"cell_type": "code",
"execution_count": 175,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(pca.components_[0:3].T)\n",
"plt.xlabel(\"Principal Component\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looking at the the interpretation of the first three principal components, they correspond to:\n",
"\n",
"__Principal Component 1__: Directional movements in the yield curve. These are movements that shift the entire yield curve up or down.\n",
"\n",
"__Principal Component 2__: Slope movements in the yield curve. These are movements that steepen or flatten (change the first derivative wrt maturity) the entire yield curve.\n",
"\n",
"__Principal Component 3__: Curvature movements in the yield curve. These are movements that change the curvature (or the second derivative wrt maturity) of the entire yield curve."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## 5.2.3. Reconstructing the curve using Principal Components"
]
},
{
"cell_type": "code",
"execution_count": 190,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 4.97514826, -0.48514999],\n",
" [ 5.03634891, -0.52005102],\n",
" [ 5.14497849, -0.58385444],\n",
" ...,\n",
" [-1.82544584, 2.82360062],\n",
" [-1.69938513, 2.6936174 ],\n",
" [-1.73186029, 2.73073137]])"
]
},
"execution_count": 190,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pca.transform(rescaledDataset)[:,:2]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using the simple matrix reconstruction, we can generate an approximation/almost exact replica of the initial data.\n",
"\n",
"Mechanically PCA is just a matrix multiplication:\n",
"\n",
"Y=XW,\n",
"\n",
"where Y is your principal components, X is input data, and W is a matrix of coefficients.\n",
"\n",
"\n",
"The only trick here is that your matrix of coefficients is quite special: you can use it to recover the original matrix.\n",
"\n",
"X=YW′,"
]
},
{
"cell_type": "code",
"execution_count": 229,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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Amua+DYB/3LCGCdfeSO0F54euWZmGTARSZXVBobLoHn8UABEXLPnZCoIgHFbIv+qCMAw7v/hFXlz470GBdlHY2DFfjLlNALgZL++QX+aAV1Ge72JVVITGzM4yPmNtO/pZfOd2pnzve1jV1fn6qiTEHHDsYAztR/pPlNfzkcUeEUei8AuCIBxOiBgThGFY0Tx1SIlLXWM1b/nM50KlGpj//HP5891T3821n30MAOULtxzt3YGDfzphLGtH3HcvM2+5GYBP/8NjfL8mFR8fui7AzunncvZqzbiV217DXQmCIAhjDRFjgjAMTVPOAsBz2tBeEq2TVMZqiKcDa5fWLm7WQ5WX4/mrlc3Vp5s6T+N2d+fbNvz4Z6Hx7Yj5+UUnTcqnRwI4dodmw5EfzZ9n+m4mm3iSpimvN/PxSicTFwRBEA5NRIwJQgkSa9YC4DlNZPpvId17HdrZw5nqXbRdsyJoqDMA3PXj5WTjdmiMbMbFG+jPnzfXHR+qb9rUQ2ogiOQfaWwEYHoH4CWDS3g9uOll+XNPfrWCIAiHFfLPuiCU4LH/uAmAbOKRkvXnXXYFAEedYZYTW7f1EScaatPXkSJVbQTW1J//jBUP7ywap7s1yGU547c35o/HdS4fdm6uEp8xQRCEwwkRY4IwhExbK50TjiWbWIx2O0q2iZUbB/ts8nks1ceEqVXoZIremtn5Nrd/73nu33oUk7/3X1Sfdx6zj5sIwKd+fFa+jSoIXWaPG5c/TpZPLLpmbvemZ4kYEwRBOJwQMSYIQ9h89hvRKNx02DqlCn4uZe3GMX/NEw+TTfyZzj0DLFv4ZdonHlc0Xt0FF6AsC8tW2BGLiprAqT+bDvy/7JoaVJmJMdY9bl7RONo1/mebW9pfw90JgiAIYw0RY4JQwPamZSgNA5WTiupsFeSTtDcHIsp1jH9XX+0R9DYcO+zY6aRDrMKM8aGrTgYgk3Ly9cq2WfDSSrKRSrQ3UNRf6xQaxWnu86/wrgRBEISxjIgxQShg+WM3kI1U4iQeL6qLWIFPmHKD9UXtBcfReUcW9XOyLom+DGufaiJi93DD5ZeQSfYC4DrFSb/tz3wFJ/Eo75l+GR+e/dV8eXbwIZxInISSn60gCMLhhPyrLggFdO8cYPOc9+K5LUV1EVVajCkr+BklejNF/Xpakzx3zxZz3LKE3rZWdq0xS6B+PFc810N7xhcsdsbZaJ2mPFIdHkj3o1WEm2uGlAuCIAiHNCLGDgB333033/nOd8hms/tuLIwpjn1kI82TzwyVlVfXAFARqc2X6VSwTFlWEfiAJfoyxKuG7qpMMuiLNKWM+rKjpo3nGgF23eee4H8ve5zUQJbUYBY7dlTJ+XmWjeXB75ZI4FdBEITDBRFjB4CVK1cCsGTJklGeiTBStNasO+UUapv6i+pOv8AEYC23K/NlXjrw9bJsi/MuDXzFyqvDUfcHulN4vtVL+cnFn7r1//LXLaRlWy+9bUlUQfgKRcGSqLKxNKz6+69f2Q0KgiAIYxYRYwcQ15VI6YcKLRtWQF8/gxWNKM9Bu+Edix//0S9YeM678ufRSYEwK6+uYfrRQfqieEUk1PfZe7aSSRrxlh40wWS19vCyu1i3pJlsJvw9yaQdLDudP7dUEEw2J8aujl33am9VEARBGGOIGDuA2La970bCqPPHZ7fz3V//nsGKRp475ZtoKyymjn3jW5g0ew4TJ04HWxGZWE52zwDvveRrAMSrqrCjwU8pm9qDk3q+4NyldVtf0XWzycW0bO3l6Ts3BWVpFyfjgQ7EWEfdDKLl1VjRObTVH8/MVokzJgiCcDghYuwAImLs0OC9D5zChWvvZ/lCE1VfF6QiOvoNbyIajwPgJR2s8ghOh6mv3W18yHavXY1lqXwA192rr8dJPk3dpApmHRcEb9VeEG3fYERfb1tQ7mRMrkutU/my++vOI5vsx8tuYesR7+NN647ihtqa/XPzgiAIwqgjYuwAImJs7NM9mCFGmvodEeLpHgCc1NJ8/Rve90l2/+dTpDb3oB0PFSn9k3Ey6ZB1DOD8rywkGgvK3MzGUL3ylx/3bOjJlz1+ywa2rmzHzQYC7f6JDYyLBXHPMtEqfjG+7pXeqiAIgjBGETG2n9myZUv+2LLk8Y51ejpbOKdhOtlIJQNV0wBw0y8FDVrMjtjEshYTesJW2HUmSj5aM+kIEyn/lxddQKLrryGrmlIuVoF4c5KLh1y9WKznwlt4bmAZczqSvHXqJ4NxtSxTCoIgHE6IWtjP/PnPf84fx2KxvbQUxgKZvg5qEjBQNaWorqyiEs93vHcTDl5fBmUViDFXc/Qbzsm397JbyAzcnT93Mmko0E3VE8LX8JztaF0c9FVrFwqWKQMsf/dlcR9BEATh0EXE2H6mcGlyaNgCYeyRGuyhOqnJRE0gVc/Zg7KML1hFTR29920FIL2xm/TWXpStUDHzGXsZlxPf/h7qGifnx9Nuc/44m0qhC9TYMW808cs+9oOrC9oXB5fVTnMonEWABzhiGRMEQTjMEDG2n4lEgp14Etpi7PPstvVUJ2HNMZfguV1k+m9HeyZV0TmzLizuYFvYflDX7G6TPzKTLFiatIIQFzd+8TM0b3wIMMK8v6ODWHk5jXOKk4AXUl7thsJZhNBOPlaZIAiCcHgwamJMKTVdKfW4UmqdUmqNUuqLozWX/UlZWRkVFd0cf8IDuG5xsmdhbLFxw3NMGKgHINN3a768YdYcoq3FP4/rOu/hl2tvC5WlE4P5Y2WFsy60b30MgEkzN7Fm8SMh4QZQP8Psinzvl07goh+cwYRpVUydN1BSjJkyD6019T2a1r5SS5mCIAjCocZoWsYc4Mta66OA04DPKaWOHsX57BdaW1s5adF91NR0kMncO9rTEfbBx2P3c9omsyyprIp8edv2LcN1KSIWL88fe05xBH+AvtY1oXPlJ/s+8/xZXPKz1zNtwXiqx8f5yDdOYe2TD2GVcO6vjNQBHgrNtde5PPXyyOcoCIIgjF1GTYxprZu11i/6x/3AOmDqaM3nQOD0pPfdSBg1PE/zKEfj+vkild2Yr5tXc9LIxkhkiVVU7LOdHQ1v5vjo934CQDaTJl4ZxXNdmjdvAGDmcQuxlM1qeydr7d35PhEV8R3+jT/Z1KYHRzRHQRAEYWwzJnzGlFKzgIXAc6M7k/1B4M/jOXtpJow6f3upiVVVKSrTxgo1aXZZvm521bFF7Qud8Z1pxm/M7c/w/q9+m4XnvTtfFykrC/V7/YfnUFVnrGdxP+l4NGbaZFNGsN9w+af549e/TOvWzZRX1zCuYTLPRjexNLqhYCQFeGjfqoYnPomCIAiHA6MuxpRSVcBdwJe01kU5Y5RSlyqllimllrW3txcPMMaYOTOIUeW4pXbECWOFrp1raPA6qE7ZaC9B88ZV+bpSLvJuQUiJJ2yz7KizHhOmTuf1F16cr4tXVYf6zVs0Ds8zfSNRI+KUv+vW8wVVf6f5bg/2dONkMkQj8aLrG4EYiLF+d7CojSAIgnDoMapiTCkVxQixW7XWfynVRmt9vdZ6kdZ6UX19/cGd4KtgUuPm/LHjya63sczCzb+iPmHEjecOFfrFn51TIMYG0yZCvs6aMjsSzdfFK6tC/fo7O3DSxgJm+SIsFxBYe8Uxw9xshjmR4wpmYuYyr/Yk3MwG9kw+A4CV3s5936QgCIIw5hnN3ZQKuBFYp7X++WjNY/8TWMM8HdlLO2HU0RqdtvBUBO12hqqqJwbC36o2/l4uwbJgOpsBoP3Xq0iu7URZFrnklPGqsBhr2bIx7w82d9FpACjLiLKhYszJpNm+agWVXpB7snB51E09S1elv0Qqy5SCIAiHBaNpGTsT+ATwJqXUSv/PO0ZxPvsdT4Jzjmn6XIdVxHEtCyf5RKguFg+c8id/ZREAWVUgxjLB5oyuP21AKQX+511WERZjD1//q/zx2Z+4BMC0p1iMDXR1oj2P7mQQDDa3PDqQ7TZ9tAmP4WkRY4IgCIcDo2a60Vo/DSXDjB/SlJUFCZ67k12jOBNhX3y+cTdnr4LO8mJRo9sz+WMVtbEqo/QXxAjLWcaAov/SNG9anz+OxMpMWqRcU3+ZUvnLlJ7nhTI1PP773wAwtXIeYJYhXTRRoCo6DoDKhIny75VIpSQIgiAceoy6A//hjOtlSaclvMVYpL3ffC5TujTRvSwnx48ez3PPPce4zx1L7LzSkVeUFf4/RSYRCPJCIVZIzmfs4euvYf3SJ4vqB+ze/PEWO5wyKZo1wYTFMiYIgnB4IGLsAKIsl0QiQXt7Ox0dHaM9HaGA59du4Y2DCcrT4EQD5/tjzj6X8urAX6v9GM0DDzzAo0ufIGUH0fVnz5odDDZEjDmFVrMhZNsSNP/oeXQiEFIv3H1nUTtdHYz5THQj/STpzxpLqyZnVRMxJgiCcDggYuwAYlke7e3tXHvttfzqV7/adwfhoHFkz5P0WxbjsmDHTBiJd37pG5x32RVcdsMf8+2cmFlCTCaTDA4OYts29fX1xMsLQk9Yxavt5112BR/+7n8z87iF+bLJc+cz8PQe3J402c1Bqqz2nduL+tdPmxU6vz2+lN6M2fGp/ctN3WisZxt3tUlSekEQhEMYEWP7kdALMV1FLJbkj3/84/AdhFEjUT6F1ohNnarDixphVVlrLGJur1lajM2swXGCyL2pVIry8nI8z2PdunW0KxMWL+eMX8gxZ5/LtAXHhOrO//p/5UNhqMjwP72JM2ZBCaOXyv9czZixRJY1K5/jyBvn8fif/3dkNy4IgiCMOUSM7UcKxZjyYlhW+I3a11cU01YYJXYmdvG2Ry3mr+omGzU7J6Mx4zvW+9B2ADI7+7jnnnsAWLNmDY7jYNs2nZ0mDMbyiJ8bMmLE0ewTTAolyy7tg1ZWmDZpL1tXphy5AC9VnL6hPj49XOB5tGx/mhNnTaej+e/DDygIgiCMaUSM7UdyYsxpORbsFPG4WYoqL+8jHu8nkxnel0g4uGxP7eZtK8zn1VY2Ewii4idebANg0Ao7369atSrveA9BWNhIrUlt9IGvfZfTL7iQC7//s2Gvm/uOZF7uLqo79f0fBuCciy/FTWaL6mN2bmnUV3LaY212N1mleDhePJ4gCIJwaCBRSfcjWms8z0Kn6tCxBLWxBEq5LDr5Hr/+P0d5hv/c7NnyMjtWPMoZq79NfM5FBTVm6TAXdgIFaLgvtrwoEL9lWdTV1dHT04MqsyALVlWwAeCMD14Yap8TX+On+lYtPytDdvsAQznrI5/grI98AgAnVSzGcriRMlwrZsZSCiX+YoIgCIc0Yhl7Fbhumkcfm8Ou3X8IlWutUUqjdLAGNWHC7lC9MHrsvvNcntvzc143ewbdfSa3pGtFyCmunBiLzaoFoF8ni8awLIvaWlNvTalAxSM4bcXthvKGj30KgMz2YKk6Vl6eP55+zHGh9qXEWNIz1xmIV/L8yVehPI+K9gFu/5HLnE1idRUEQThUETH2KnCcHgC2bw87TefEWOFjPeroIIZUOt10UOYnlObTkyfx2zojpLZF0uyeAKlps8CP12XZNomX29El/LVy2LZNWZlZlkyn0+iUQ7YlnLA7vaOPvsfDeSPzwV7LA2P0J//tf/LHMwrEmNYaN1MsxlK274OosyTL68HT1Ow2OyqP3DS8JU0QBEEY24gYexV09mzkq/ycZ1PzQ+W5uE9aK3Y3fwNviJe260oA2NHk3BUeX7zb5Y4fOlT1ZpnWCZn5R+dzPypt0XXrerLNg7SPK23tsiyLiRMnAtDa2povT23qZvd/PoXbl6H9upfoe2hHqJ8CtKdxWoOAsInn2/LHM48PQmC4vRm8EknmPTQWMXLLqmgNfhR+ffglsxAEQfinQcTYq2DpmivYrWZyo3Uxra2b8+Vau2xgPp+cczlfnbKQx3lzqJ/jyFLSaLF102L+9UGPM9cZkXPKc0YU6Ze2kBM3mcfb8+2XZNaUHMeyLM4555z8edWZUwDoX2yWo9PbevJ1WmtOfs/5jJ8yjYbZc0itDScjVxGLL99+H1++/T4mzw2EvdOeyOejLESjiVjxvCXPcdwgWbhoMUEQhEMWEWOvgmWcAoBCs3rN2/LlnudyNV/Nn3dSH+rnerKUNFqse/qhcIEspghYAAAgAElEQVTrW5ROPImcGMtuD5YbS4QOA6C8fA/d3Y/lz7PtxoKW3mxEWN/DBcuTjmbm607gU1f/HxW1dfQ/tSc8WIlgsQA67eIpzbHHPsJJi5YHw+GilE0uCFmd15u3xlqixgRBEA5ZRIy9Cm5SlwJGjBXieU4+VQ2ATdj3yHVkmXK0cFt2h84H4+azi55yWn6pLzanOl+vhhE3jZP/wMurLwvGXVARqnc6guVN7YStW5kd4Thzyi59jc5b1uHhMW58MxUVa/Plz0Y3obDQOauZV5Cfcjj1KAiCIIx5RIy9BrrURHYwM3+utRuSZ/aQMOriMzZ61D2/hJXHfY6O8ccAEE37OygjVaBTANixIESFzhQvE4bGq6szB0dUDNtmqBiLzawJNxjGMgbgDo2pAXRY/Shlkdv9uSEWQ3sixgRBEA51RIy9Rq5SP88fe57LoAqsK9EhKW2amsJO3cLB47naI+gafzSrjruMgcopqLT/1VdlaJ0gXlkNmUAAeQVi6Morrywa7y1vPRkglC4JwjHHcqmPwPiPRRuNcCs7cpy59F5SIq2KlP6uKJRx3AcsDbgugxWNeLb8lAVBEA5V5F/wArLZLN/5zrd49LFHX1V/rcPqK9Z6AgCdjKebcaxfv/o1z1F45XiuS7X6YP78+ZO/TmPfNDTguBZu+iVSg/146eDzyxYsMVdWVvpHgUDr7b0GKBZj3kDgF1hoGet7eAeDz7UAMP6CIwFIre3EHSje1FF+fD290cLdnOa6E71qf/nUF2Me6MEYz53yTRLxs/bxFARBEISxioixAjo6mnn9G24lm/38q+rvuuEXs6ONleQL6jd8Xt3AxHqxjI0Gm9c+h1s2N1QW1bWsn/8xXnwiCC9RGF+szwqHtqivrw/nGtVmyfmmm25io106flxieWvJY7smlj92OlNF/bTjMTUyMX9uYteZZUrzkzUir24gQnOkAYBsZGrJOQiCIAhjHxFjBbiuCW0Qjb6yEBStra1kMhm0Z17mdV6SCJC0Y6F2DY1b98s8hVfGMw9+CQDP7UTrIEZX8+Qz8lkRjjn7zbh9xZ/7RRe9j0cfm8eHPrSIz1/+r/lyTSCinolsLHndXLgLYHifLr84ubbTxCnrz6DTLqsyWwu6BiJwVtV8cpaxuV0noVwTTFZbkt1BEAThUEXEWAGZ/n2ntSnFqpfP5P77v4HnuZTpFK/P7sIB7po8k63Mybdro3E/zVR4Jaz1qoh1PUim7/eke0zUeyu/pGyWFesbZoZ2QuaorNwNeLS03kJFQfR8zwvEmLUXf63Wa1aYg2F2Tubo/IPZNZnZM4CXDFtYz3t7lGgsga0tjh13KpPj5nukUUxr98WYGuKgKAiCIBwyiBgrwEmZOFOub20YKZalKYs/SDaTxsEmWhAW4Zvqx/ljTx73qLBou02fWhsqW3n85QBoP9/jxLXjS3dW5jPT2sN1g+j5WgfHdjxKwxcWFnUFyO4Z8IcZRowNMWgpS+ElHeZUT8uX9fffzKmn/JXp3gQAokqjtbHijRsw8/P08CmcBEEQhLGNqIMCso6xdmj9yh6LBrSOkUomcVWUyDBLUoPpca91isKroLs2/Hl42YLk7V4fZVYFdqL4M49Go+TWEdvbH2QwEWRb8LzAiqaUIjqpIMRFqV2SQ74Tde8zPmyFOy4BtOvhJZx8Lst8d8vL7/DUXi/pvt+bcoy1rtwb4G9//n3xdQVBEIQxj4ixApysecFq75VZxrqYgOtE6e7tACBuxUq2SxEpWS4cWKp7wuanzMAdeE6zOfH6mF65oKiPbdu87nWvY/XqYDNHOh04+1dWHpk/tiwrFDPMihd/f3KWMa8mwuLFi7Ea44ARX4XorIdOO3hW6XRIebx+cy8xE7ssi8vr136pqI8gCIIw9hExVoDr+PkKX6FlLEOMiso2Uk43AGUqyvfmFe9u02WaJUs/9tonKowYx3PYap9cVK693GedojfbHqrbZrXium4oEThAOmV2TcbjU4nHJ+fLLctCFVi+VDT8/dFa5zcKLPc28fjjj7Nm23pTOcQy1nPvFtClg77usk1uywrbxLJLVEyip7KadO9v6dI9vHPalGGegiAIgjCWETFWgOMvU8bKEsO28bxii8V/qF/xIO8gkf47AGWqkiMr4kXtnuN0Uqln99NshZHQn+zl+I27UfakUHl28F4ALNvDKvgZTP7Gqayb1QVAJvNSqM+OnddjWXFsu5K2tvspKzM+hvaQJUW3e0imBcfDaTXfqUydL9p88abdISm1+s2Ggmxy+M0kx40/G4CdM95Ciha014PKJuiXwK+CIAiHJPKvdwGek2QZJ7ODmWzbto09e/YUtfntb79Wsu9tXERarwEgpsooL/FifEK9Zf9OWNgnPS27qEpl0W7rkBojqidOK8dSgZiyq2I0NRkL2IKjHigaLxKpYnDQhLKYO88I6yAobGn6nwy+R6q+DIBYLvVSgdUsNLsSuyPjOrzMXd++Mm8/szxF1JHwFoIgCIciIsYKcNwUV6v/5Cr1c2677Tp+85vfFLWZfcSfS/YtJ0EbxvrStXUbL379C8y2i33E+qnav5MW9kpP227aKkvnmdReH9Pm12LbRhjldkTOmjVr2PGUCtId5RLFV1UN+UyHhLFIrAh8zdwhuSS1pmhHJYBTVrw7MhLvBaA/ayx37fUn4Njm3sYPKH58o4S3EARBOBQRMVaA6wXLS6eedhezZr1Yst1kvYfX6ZVcuvPxfFm/quUb6icAZHp6GWhv5VuVwUva9pc3/51rD8TUhWHYuek5UtHSFqN07w08f8+dRPzgvLlckbFY6Q0YAFaBGGuYZKLfqyE7JYvCWBSc5qxgL6xabgo8bf4MIZEZKCrz7AwazZ7BTfmylLclf5GpXcNOWxAEQRjDiBgrIO2EU9NMn7GmZDsPi2jKI54pHcLC9v2AetaszJe5lnnUCSWWsYNJe8dWnNgkGstn84GZX8KieKdjJGIElvItWuXl5cOOp6wIdXWnAlBZYUTb1q3hzAp6iLhy2gP/r5zP4e5mf+lSQ2Z3f7g9LplMsc+YUhoXD6WKf7Z6uAj/giAIwphHxFgBsezZI2qnfVOH7ZV+AUb9HXJzs9mS9cLBI9rSz0DtMZzd+CGiVhmn1r+zqI2l/OVk2+Lee+9l8+bNTJ/eX9QOQCmbSMTsZuzpfQGAVGpIfsm9uG4NdfYfXNZC/+O7wmWTQSnzHaqufl3BtT0cPD9ZuF/mb0yI+HlQS/mfCYIgCGMbEWMFVJZPJ7K6G6tp+N2UKcpIUY6lPSK6tBjTfrkdifDkI/3c/0TxkpNwcNBJyDnrA8yoOqqoja978PBYvnw5g4ODNE5eWnI8paI0Nr4vfz5ligknsXnzZm6IP8ogaV60tnBP7IWivvGjJ4TEUoI0me19pDZ0h69xfB3KjzNmFcSsa2jYBmhsXzy6mfX5utz/C9ZskWT0giAIhxoixgroqoTIngSxl7uHbfN5fkOfqkWhqXVLL2eNHzRizopYVLjQkNY88w9jaVG6tDO5cGAoH+wFvXfHdksba9W6LesLSksH/rVUhIb68/Ln06dPo6ysjGefNTsr260+Xoxso93qK+o74cIFtLcHMc2ejIZTNEX8KP7JahdLGdGmVLAJZOq09WjI7/7MDt6f3yWaW6aM9UoyekEQhEMNEWMF7IzsO79fUpkwBjFtEx3GMjah3wivbHUgAqIaXt+/khp698NMhZGyMVKFZu9iLEoZRBSPPPFYvqzwk50396r8cf/AupDDvuftIp1Os3mzSZW0YWpnvq7hi+F8lS3trXR3B0I/rcLft4Z/O57Gr57Mvffem1+mLNwwACYKf2EojqDczKnPHd6qKwiCIIxNRIwV0J4wyZdzGiup46xoLi2eLDSRYXzGlJ9WqWxI/Km455CiHC3WsYPGiVvH4yQeCZXNrDomdH5U3angaObPn58vU1Yg4GbMuCR/rHXYDzBeXhY639VeEFNsYrhuqKO/Ivz9seIRIuNMsOCcGCvMadnb00BftgurhAN/7qvY5gxv1RUEQRDGJiLGCuhO+pYK20SQ+vzDP+b9v3ia5TuGvOC0pnlXJd2Z0rkmvUyB83cu4HrUIu55pFWcjCPWiwPJ5rYB1jX34WSz2Lo4TMVp9e/ivKmXFJVHIsHn6TjDR8AHWDD/+wAcMdvFtktv1HBdN7/0CPDwww+H6i2G3wEZiaaLymrr2vC0hyrxs+2rmcGuqW/EtqJFdYIgCMLYRsRYAd1pI8aUo3mMIFp+U8+QF3PGY/eOan7XPa7kONms8RfSnkv50RNMoYJyx1hbPvryLj6xSnx7DhR/+cUVPHHtZfzovuVkbKtkIvDa2MSiskwmkz+2rPDS5rx53widV1bOBWDrth9w1NGL8+UVFYH4chxnrzsrrYJl7tjs2vzxggULmDZtHQA9PeGNADWxCUyrPJKIGiIytcemeR8sinkmCIIgjH1EjBVQ0zWYP95AsOuusizsoxNbaaJrDo0nlUP7u/dcxyU62SxV6oxH1DHlS3vTPNxZ7OB9qNKUyjDgjJ3o75+P3cnF0fu4/KXzcGybcbFJw7adt+h0AGreNjMkxuJxY718w+uXATBt6sdD/Sw7yD1aXd2RP04kAqunEWPmO1L3vrksWrTIH9tfiiywjMXn1oXGd7JzzPzmfT1U/qf4EnpVgrhtvle2inJ03Rn5bAAqVWxREwRBEMY2IsYKaHCDeFFLVBBzLBdRPZk0L12rx7y0h3t4nu8T5rkO1W+aQf2lxwEQOUxjQJ34zFreu2ITTU13sHXbL0dtHl42yWP/uJm3TJ/CqbOmk/IsmusXwDDLgf9+69946/svA8BpTZAtERcuGjXWT8uKolSU2lojqGwr2Emrh9nI4bpu3jLW6nazbNkylFL59EmF3wbX89ixw4SlyGQyNEx6EoD6iedy5hlPY9sz6GifYcayejhm3JkAHFV7Kq8b93pmVzQCENnZstdnJAiCIIw9RIwV8O7j5gUn6cDSszNpxNczz4atFB06gtVS7P+l82LMRVmKsiPMEtS2ign7e8pjhjUDKe5bfyN3b1u878YHiFu+/34mXvEDnKz5Wp8/aQqODV3pJjpVP8/HNqMLJFDXnRvR/udccdIkY8naC+e8cS0nnfgngHzgVwCtS/+MHMfJW0/vWfqA31bz0Y9+FIAmuwvH3+m5dOdyfve739HU1BQKIqtUlHh8MmDnY4+tsXczq+oYJpZNZVql2XQQ83ddOvsI4yEIgiCMPUSMFVBZN4Uz+54BQGWDHY/JrHnBOdnil3XspW6+q/+TO54Klh09/wXbumVTqG0qfvhF5E97wXP6lvpvfqy+OWpzqX96D26kjjnNRgCVZQDtopTFY9HVrLJ20K2Cpejkmg6cbrOsF51cWdIyVohSVt4nKxoNlhWHE2N79uzJL1MWBnudMCEQ5R3KbPZ4YdfLAPT29obEmGXldmQ6RKOmvNMyfc6d8vG875vy45I5yE5dQRCEQw0RYwVkUg6Vjv+yLhBjGd/XSw/jjV2+x+KIhOKi7a18fVVP/sW79cXA+brmbTODmBmHEUu6x052ga6J57H09O/z8SfquPgRl4pMBHCwsOi1jAVzcUGgVWVb4JrPVsXsIstYJFIz7LUKI+OXxytLtvnb3/6WTwJu2aV/anZFlKozpoTK0uk0jnMsllVGJGLGdt1d1NR0lBrCjO+Hu/D2EVNNEARBGHuIGCsgk3Sp8HP8WYngxZzyX9ipYR7X1i2nAPCFDRW8v9nGw6Wito4jTzsz38aKR2h0u0L9ektY2g41tibHjsP4QIVZZh6XHMc7X9C86aUoTvKpUJDUnFUJAAXaMWJp9drVNDU15aui0fpQpP29URav4Otf/3rJOi9lxJFllf7u1H/qWOreMyd/bts2qVQK21JUVszNl2s9NTzukFh1uaXxDc0SZ0wQBOFQQ8RYAU7GpSZ6GgDR1T358qwvxv5qnTqicbT2KKuoNA7cPmVH1HJe3xOhdu9Zsfk1znj0mV524ONaacdDO3tfftNakyKJk1qBaxnxdeY6Y72qjNaV7pNy0Z5Go/nL3X8N1XlepmCJcO/EYvUhsRWNBs+k+RRNZFIFVsTMqbKqk0cfm0M8XjoReTqdxnVdLNvFsoPrKxbgOGbcBq+mKGBsMrODbPIpTmy/Z0RzFgRBEMYOIsYKOOHNM4gTLypP+UIgQXEAUYC0Doe+0Ggs28ZzA8tXdFIlPdvDYm7DYIpDnZSb2Xej18ieby2l5SfFibcL6U9liQysxEk+Tn/MfB6uHcNWEY6pO2P4fo/upN0OCyOlXFy3FzXCAKplZQ0hMRaLBd+T+154mMYrTsr7mk1uNAK8oaHNzNENLyvedddd/hyckBicNn0ekUgW0LRZffR54cwQlrJxUy9Qrg/975QgCMI/GyLGhhBzi/P+5Sxjw9lmjsocVVTWuXsn21e+GCqzy0pbaA5lBjMHflns1uiT3Jl8aq9tHl+2Cg/jgO/Y5jN0IjHK7Aq8IZ9cmix6YiCYeu3wjthPfsqEkGhve3DEcywMtmrbxd+hnFiLxczfixYZYT5UjOXIZnuJ2FX583i8zh/bF/iR8H8Mcj5jv6upRRAEQTi0EDFWgJdKESnxSNJ5MVbaAX+WDkdzHzfZOGRn02ErhUJxqz6fi/UN+2O6r4o/NXdyW3Mn1+xoZXAYIfBKaO9eXlTWkt5/u0a11iRVhi5r7xsFGh67NB/RvnO62a3o2DHiVgXr7D2htjfHn+TGgQfy51kVfg5trfeb/vtIun3iwtv8OYZ9//r6igP6trUZS5hlm2vZEROp33Gc0E5Lg8ay2hiMzaM9Y56l5Ufcz+WsLMprqUwqp84SQlAQBEEY24gYKyC1ejVlTvEyT84y5vovQB0Pv/A+xSCJgp2WR552Vv440RcsJ1XHjKXDKrDUPNlV2nfoQPGl9bu4Yv0uvr+1mb+19ey7wz6IlM8uKjth6ZrXPG6ObPvI8njeN3ki2t/h2GefCBgxFrXjJNTel1KXqvX54wsuuIBI1FiXYrHxe+03bpzZuNHe/o8RzRGgstIsg1t+KArXdfE8b0ibbpTSvL/5XF63xH+WvuUrEGNhLMx30nYPz8DCgiAIhzMixgrINrew8OXrisr/2tLDz7a15CWUtsOvQhd4Foc0Gg9N2lOc9oEPA5Do7WF3d4KmniSnNR6fGwEAqz3Fh57beIDuZt8M7MMpfiSkh0kJtb/oHRhZ2igv7ZKN5kJRuHjKZsvsdxBR0b0m5B7K7NmzKSsz6ZNmzbxsBD32Pfb69YHYmzLZRMrv7DLBY13XLbKMRWPF/yEYmhzcGRLCIrdMWZ2ZPoI5C4IgCGMJEWMFeIODVA42o4bqC0/zk+0tuJ7vw1MirdG3SHIu/VxHmktWjadu1pEAOOk0Z/3345zxo8eIRM1SUs4yFnuxk/jig5u+JvZMG9EXTbwqdz+kZ0oOk5Myu59EmvZGJhiPXNMPfggLrbM8ddZPyEbjRKwY4/3PrZQvVyGf/exnqaysRCmbWKyeyZPfv8/rTp16IdFo2IIWjSWorW3Nny9dujSo9L9c6fRWf66awcHBUH/bKg55ovKWMdN/WWQL2602+pVJYm/7y5Tzd3sllj0FQRCEsYyIsQLKzn83qRnjeacbdo6ObuknsrEX1zEvvGFivwJwL2ZJLOO/HJs2bcjXPd2b5KFnP8LJPJsPBnqwsfqy2O0mNpizH17aveksVokUPMkRiqh94Y3wOVV0pYlb5cyvPQV0BtcuQ2uHOdUn4KGpqu5gwVHPU/jhrbZ3hsZobGz0r5kJBXXdGxG7CtcdIJ1uY+7c51DK5cQT/85xxwdLl4WhLmzLLFPadg1KGavYo48+OmQeJe7ZF2M5MZdSWR6JvcztZUt5PLoGz8+fevbLDu4ofbcEQRCEV4eIsQJ+8rd/Y0+6mbgutqBEtg3Q5fsSFVnOCsi5mb//Ly0M2hU8dtOv83VXrG/ijr4z6Nw+h2Oal+XL71vVxMHgmh2tofP9IZeaevopp9ivazC7f0JeaHdks+wv05xUu4ATxp/DOH+noY1DfXwaHh5HHbWY8ePXUlEZ+Mk9H9lMAiNM58wJAq9qL5sXY+2ZLHOfXMWLfcZ69enV23j7smBp2XEH8LwMTy85nclTNjJ79ovEhiwzJhLB83E9U+e6fRwxZxlaa15++eVQ+/ETniy6v9wy5amn/oV4vA+vQFRusVtoLQ82TTj7YWOGIAiCcPAQMVbAsdHTaejVjO/dVbK+ya4yFi3fovTOORNLtstxx5TzWVZ7YlH5LbvOY8vqIAXOy7t7i9ocCH708IZ9N3qFpOwYFSXEWGI/xR9LDvSz6OS7Of74vYeZiGUg4luHyK4zf2eMyPGUJh43c5w/f0m+j43FNtvscuzvNxspBge3kM12o/zE20u6BxhwPa7b2Q7Afe29rOgP7reh/m2heUyYWGhtM0Kyubk5X9LR8Uj+uLa2Dc/zOP7449kbWuv8MiXA7NkrQmIMgt2VWlm4+0h4LgiCIIwtRIwVsOj0j1KT1CxcdXPJeldZxF7oQKU95jbu5tKF0/Y63kCkimfHF0ft35YMp7apKT/wUewBopsLdm56Ou96nvX0q/IfczzN03oy7WoSX9Y/5Cr9bS7XPwOgM5PmrpYuvNe4FPry4hWUl/dTU9s+bJtM1sFzJ+P5y6W5nYXKbUWjWR7Zkm9bVRXERdMEz+CDH/wgWmuefe6tdHUvwfIDvubCh93bHt55+pIvyOrqTg6V50QfgGWFrXozZoZFq+fa3HPPPaxcuZJoNMrll1/OhRdemBeCOX62vZUlA0H+y4n1O4tDsPhiTSsLxzn8EtILgiAczogYK2DGxBrWz7GZ3tfMCdFdZBaFLV+T+nuxeozFp7qnjGl15SMe+/jeVcPWpbMHflkpNeQaZY8309ltnL+nL36Jj6/aygPtPexJjdyiVRin7ESWcQyriWPG/F1TD59bt5Obmzpf07zXu0HgXD2ML1RfbyeZyncFYswXJpHoHAZJDxvawlEejm+9qq2txXUDR/p8XK9hdkt+d7NZWt6bb1kuDEWON51zQuhcF4ydzWaZMGECRx55JPX1b6GiIlg2/en2Fj6/uzHUd7ob/m46/tq5tmwRY4IgCIcYIsYKUEqx9Kw4Nh5nxPvxJoRzEyY2Bb5AnhuhKhYpOc6J44rF1Um9K7hsRnF0dG1Bej+EmNgXiUx4TsrRPPbUTrTWxB/aw5PLmvjU6u2858VNIx4zVUIclfk+WH1+EvSNrznlU3CN4fJTtnTsIBM/qkCM2XjZ3dhWlLTKFomiHEcccQTRBSayvWVZ9PW9lK9Tvsh6urt0HLjUMBsUCndWWpYX2sEZiQxN7l2QzzKWYNPmH6G1i+el9yry0ulynCGBauOejbInopVNtkSsPEEQBGHsImJsCLurjLWiPFX8EtYFnvseGmWXfnxHlchIE3dTtBYIotpZSVJvmgyWKhJjyYzLl/60grb+/fdS7U0VW0t27ulnd7dZOotuMvG89ryC6Pndvm/Sp/X/5ssGu40YcX1hlH2Ny5SWFTyz3md2l2zzwpZVgIunzXO0VYTMwB1YXh9ZXCZPDsdymzvvGRoa6igrK8OeaiLh27bNli0/zbdxnH4ynscfCix7ToH4TBZsLFAqEOWum8wf/8u/XBRKd2TbwVIjgNaBZWzhwvvZufM3dHc/i+dlUGr4JOW93ZOL44xFomi3A08pMpn0sH0FQRCEsYeIsSEcnzX+OlYJK4xVkFpyWvmkYeN9zq2Bn1xwXP78wt1/wsbDSQSO1ZcceTNELbAV6SGxuq5/cit3r2zilO+HQx68FrpLiDGA1//4iVc95qWrdwCgCqxX/d0NAGSyZl9pxn1tgrJQjD3wcLETf38qS+OK76G9PjzM8434ViVLD5BVDtFoeA6TJ29m/oJrWLduHU8++SRKKZRSjBt/Zr7NwMBaHuoIB5xNFFjDEgVirNCK5XmBGKurC3JLQpA2KWc9K7y3sjLTz9NZPC8D1vBiTCmPhAoLLu1pbBVhoMzi1mc3D9tXEARBGHuIGBtCVfytADQMpHiPvitU53jBklNFJI6yFN+h2G/s+HGKDy6azjXn1HDZtl8zIWucxi8sMy/Yi8at4WhWE9FZtKVYvaeP3mQglpbt6Moft/TuH+tYX3pkO+wU8FBH74gCh25MmLmlCYSD8q1HgynjUzWQKL0zdSQ0bd7FuPFB2I+NkeaiNl0tO8lms2QH7iOtPF6yt2P7DvCWipDFJZ2p2Ot1xo9v5YVl56O9sG/Z0E0NiwtSVxXGUbPtsOjK4XnBZxqLJdiy1VjeqquPAaCmpgNrSIBXhYXj9OOqcsoebya2tK1o3PpJ29keDYdDqYjW8fapn0Zhcf+KLUV9BEEQhLGLiLEhvPXNH+DCK208O8KH+WOoznWDx6U1eAmHNxPlXwlbMXrbkmx8oYVjJ1VgF0TzmhKzeZoaTlUZFOCoKFbS5eU9vRz/3SBI6FObOvLHD6wuFiCvhpwY0zErZNGbPt4IFa/CLLVp4OKXt/FYVz93tnSxJbFvMZgmnj/OuTK95BkH9Kz76pfMUj2DzJw5/MYHgK27d3BTbBza62RbnccL0S0kY+YGLWXzRHQNTtZ8PrFYQ8kxjj7mIfr6VpJMhROKr+pPgmt86uydA3xmzfZ8XeEy5YkLb6ah4R1F4zpOP1OnTvWv8TiZjPlcjz3mf/Jtqqq6Qn20dkmnW1DRCaiMh9UfCLpUwXOOxYbszMSjMlpLc+Pp/Cx6bcn7FARBEMYmIsaGMHH8FBwbypPGIlEVG8jXuU5gGVvWP8j/XfVJAC6eUMuTV57Dd887glO6X2DVE008fONaLCscPNZ1fStI70wSiRqGY0Fjdf54cu3Id2zujf6UuXbmxAmc8565ZBcYx7ZdXealbiUc4g/tQQJ3utYAACAASURBVPm7RVvSWS5ft5M3vVA6NtmLvcHOw4GNFivbjgVAE77n1+IzFokNDflRPNavH36EaR2mPOfUXlFjYrgdOe40PKVR/nJgJDLUgqVDzv2eFxaO/7urDavdiNHounAsuFnlgQCvrJzLvLlfK5rbsuXnY1nmJ1ZVFSxJRqPBeneh3xjAtu3Xks12ESkrDpvSQ8E6+ZA1cu0/m76amRxhhUWlIAiCMLYRMTaEcTXjuby7l94K83K76pSf85nX/QEUqAJryE7Hw9FZ+MR4Jn95ETMmVPCB4+o5tSeIrN+0pTs09rYNy/0jxUD/hKJrF6b+iUVyuQiD+q7BDD95aD2ZV7H7si/nmB9R1NSV404rvXQXXW/iadVFjagaLhH4zlwIjJTLo9vP5pqVl3Lf0oso6wnnaXRfg//+UDFWalfkd2PXM63TiCzLFzb1qh6A2jJjCbP8fonE1lDf2bNfpLw8EFmuWxy8drhfyBEVYWvocLsfHX+Tg22PLJZcX98KALxIINajKzuxtw/gEIwRjaaob9hKebnxa/Nym0u0h6tGnhhdEARBGH1EjA0hErGpWXgvyTLzcptU0cFpk5ehIhqyJZz6ozbKj/weJLU2530dYR+k1T1P52s9bVGmw0uAOb+xRMZlXoMRGF2DGXZ0GivU/y3ewrWPb+HuFa/c8rGlzVj4tG1xal0lWMO8sP1bSO4jDVHct/hM3R3M5a8Di7ih91i+ob+ZL2t140V9R4o3ZGPD9Omri9r0uzbnrvId9v2vc85K1JvtAjSzZr9Y1A9g8pQNNDYGzu5ewU5I265ialkU1Rfe+GC1p5janeWeth5aCnaeKhUreZyL+aXU3pKUFytWTwU7L+3WFNENvTgFVsdZs1ewYMESTlp0D5VVnQUR+T22RyP8x2/u5V9+etterikIgiCMFUSMleAjbzyB2JDMjXbUQ6UL/L88Y/Hobg7EyFAxFouHrU+uv5tOo9GeRS3hqO57eowYSGRcauLGCvK1v7zM2T95gln/+XcWbzBR6De2hsNuPL+ti6WbO1jXHN79V8ifl5o0PV+Y3chbK5rCJrcCdJn5SjzY0Uvs+XasPSWsRQRJxk+wnimqm0RL/rgl+xrEmBt2bp85q9h/7O74NNxIOZbdgOU/d9cXJl3ZVmJlCWKx0n5rSumQc79bsBPyxIW3cGJVOdEt4Wcde7GTzufbUN1prtwQbE7IRewHsO1gadnz/GVgFY5JF4vV5+dQyuLX01+8PFxoGcv1UQpOPPF+7Am5+HAen5nUwE/3fJzfDny25H0LgiAIYwsRY8NQ1RGOCRWJeqhM8NLM2Wwe/N+r82UD3WZZUlnmBV/TMD00RuEORU9bxAhbztY0mSWzVNaltkSKpA2+CGvqTYbKP/TrZ7jwhud4+y+e2ud9ndVQTVvTraEyt7Gc1LmTccfFUBkPe+cA9zX9f/a+O8yuqlz/XWvvfcr0PpOZlEkPKZCQAgkEAgGpgoqCBRELeNV7sf3Uq4jtqhdRsV9BvcoVVJAigoDSSxJIgSQkpLeZTJLp7czMOWeXtX5/rN33PjNnwqSg+32ePNln93Zmvef9vu/9ekB7VMS29oTuJ8sYaGcG21qnBZYd7nUS5QeR27x0JAwNdI+4zloli4FkBYopg2S+zrYHF6FQ5NwFBJQyO4QJAIbLhkNJTMBjb7SFbQYAkPekkGVurzHneSUSTt/R2XPuNE/FS8bmzvkpAODcc8/CjTd+OLB/JTk1MO8R+j7n3H0EjhYIos45g8yAxwsLcG9xeJVnhAgRIkQ4uRCRsRwYKCjESy9+0P4sywaQdcJm7lY2u15ZhcHeHvR3iqR/QkvNbbyhKSt8xsDBmYR34c+e5V96cAs45xhSdSix3I/m8S2taOkZQkcqG8gfS+XwE5s5oRSsPIakJIHSGP6bfw6sTBAlqTUNyBSIUdB+Dcr2PiSeHb6Ks3dIQ+zVLhxJ1WFcYatn2Y/WfRLgHKRXRQ6j+ryQTgXJGPOFT6uyFIPJClw8/qO2MqYTAzJRwCmBJDv3o6HhA55tOzvHg0qO+qbrKSTi9Vgw/27c1jxoN4QPAzEY3Ol07jBkJhO8d5rmvUeWkjapsQHZ7JOB9UsrzwvMe5U7DcVTKW87JG57ljHIBvClmip8p6oCv121P+c1RIgQIUKEkwMRGcuBASLytJqbRZWgouhwGfCDu8J8j/7oVvzle9+EoVpKl1BBlISEumkzxHQ8gZIaEZpKExWMU5yBl5E9qwbabKdKbkg1wDjwl57cIUcAOPt7z2Hxd55G2tfm6Klt4WpOWjXAKUGMEgAExegHyfjaNo0i2b6506mmPDJYF1hOu7KIr+0AORAe5swLVJxQ1+tn2rMM1Ru6nDkkQVVEWHCvdATxRAoaDFzV+DlUJMdDlhz1sab6Ynu6oGAKqqpaMHGik4em670oKp6NiopleL47BcS8ZFpqciprYXCs6nU+E9f7YBgD8INzodDFY7Xi0syEf840tBwKNqbXQxRF2fWsA95p9nUKMmbhW3/bFthPhAgRIkQ4uRCRsRxImGauTQcW4KUXPwhKvExlqeElMqmuTjBzHjEbVTODo6RSEDAtm0FfuyBK1azE7kvIixQYNU5eVUdKDNpczu/R9Ka9oc6v/fWNwDqHetNobhuA1JVFjBAcOnQP4siCVXgrAqX2/A1mu3xmtAvlg4jDIUqnHxAhU9Kv5WUgGwZuepT9T+P78AQuBwBo7uvVMqhKpZA1ez5OnLgFS5Y8DJ4ULYx0GB5lrKJimT1NczjcMzNUaXAElDFlh8vewiwTDbs2d86Y+OyQuvLypQCcsCZjKkpLFgT2ofJg39NZyQTOPnut2KfPLJbpJrnT2yAbwGl7Gc7czlCAqE9lhAgRIpzsiMhYDiSTxb45zqD7NcRwgy/8NtTX6/iImVVvhs4w/6LLQvfPmevWK850u0nGIIcn2LNiby7ZH9c2ez4PZHWPRQYAtPc7A/Lh5jsAADFkoU0X9gnaDPP/qf5rFvjY/22wSaKFV7c6zvAfq/8b5smtuC62BUskcaytXbPFQp0ftb3FM6+vQivqsKN0PO4hH4amxaC6TGibD+zGuU8WobNC5FcVl5hmuWb+1AvKFsyatTqw39LShdD18Abg3T2i4pWBQ94bvg4AEPOiNvYHlT8/QfvgdU4O3axZ3xXbm2FNzg0QqiCZmGgTtBXnbkVaCzabf6M/jXisCkAMkuQNR1thcz2zBhIDbv4zw+ceZtiW+EjOa4gQIUKECCcHIjKWC8T/0RlgK0GRUoNtahwrBlMZ0zkmzDkVn7/vb571qnmJ7Q8lVie2CevVd4rqRO4iaPr4ApQUCeXDqPVWJ975ovDOqipywlpTvvK4Zx3FbGiuzSlDZ+u9AAAZBpCQkDl/HIzGIrSeNx/GZEHG9HpvCOzp7W1Y/J2nPSTvSJsIU/7v225CpTyAD2VW4APq2fiA5CVtNKVhncsg1g+NcXSp4a2aONWhuSoIKTWQGRwE1xh2tqbQet+V6CgtAjctQnRTHdqfED0zDSUd2Oc5yzfi9AV3I5MJbzpuIUmpTXznNoQY9Jpk7N2b9+KZLn9I2cvUe7odQihJQpGz1VOuoq3tEaQzzVh65tNYMP9uSFISQyFkDPY8FaVl3nA0Jy5T2fw6X0WIECFChJMEERnLE25u9kbX81jX+XhgHduKwRxoO1uCysqQ3o8yXojaOq8BKSv15QhJzhF5kYLyCaZqpVD8/FNn4u6PLgEANJSJkNjvP3IG3rWgIfTcNTPpncclKHAUlVKqCVXOyneSCDIXNcCYHF6FN+Urj+Mjd613zsv0KosrGhRIkCFhglqKZfVr7XWIynDV6u24cct+DOpBgvHZHc2Ys3orWEi4r6ys1dMCSJIMHHr0dRy6ZTU+/6N7cWutguI0B+EZURRhmr5axFlxVRxOnfpFMU8pyRmidGNFRTFACRSZYuuhYP4eMThoexpDBsONrjZJAMCYlw1RKayLgln56VLoksnxdig1zOeteJsTJi0q8la5DtIhdEGc5/VPv4mqiQgRIkSIcNwRkbEc4MO4mA+oHbZnmBvM8Cpju9Y56sXy918PADg4KPyjjKxXfeKFwRwhC8aEQuysVaBPKITRUAjEJSyfXo0pVYW2N1lRXMZt7z4Vs8cJFcddZalZcUIKyC4ydoUZ1ru0qtR7LlLua392RzsypkKjm6TNHVGlhGCG6k1gj69qx5N/2IZv7wya1f5lQwvizx6GGlJ2OXXqBnyD3OqZJ/WIY/+O/BK1u2RQSIhTjqeUzQ5hNicmEKcwonHSx3NeUxh+1twO2pWBNky3A3lXP2hbGnLWuw7n3hCipgWrQq0w5e7d3w7ddyZEGVNT4ZWyAKBRDX9JrIdMYliw7020PYgQIUKECMcdERnLBX+Y0pXAT3lICAnAqnt/b05JkOMSpi+utZcpCaHwbO5+DgULatC73ddYWvE9Ckq803EJ+uwyQCLoMxWm2hJHNVo/OARZorhqoehp6K6ytJUxQqC4kuxj5jURIvKcbuCiwfRNM+rBYxQsGe4a39Jjhv9M0uZeiwCI6eFk7uGHdgTmKdt6QTSO3kx+sbU9ykGskXfiKWUCbnqUgRMJhPXjoNQFq9yVEiZsRKhI9q+rfQfSBsMeV77Zaaf+JnT/8+Y6TbbpgDgnd69QN+igjtimbmjrOzzzp0/7iudzX5/oAFBQ4HiHWWFKCw0N13o+p9TgO8aKchN2ywS2SCnzzN8cjx11AUWECBEiRDg+iMhYDiQoMFd3TFvdxZS5yJi9LiEoLo+Du3KsZp11LgDhNSZXJsC1wsB20+uE0jR9xQSwqjiM6ridS+ZGjyZIwsv7uux5n9ot3OALTTuGIc0hN49vMX2vJOIxmo2ZA7jOOThXsQLP4v/4Nfjy1HHInjcO6mLHy0p3Jfe/uEuQj1MgKjf7NYckUBBQAF878zbccs73PeedHtTAOIfOOBjj+MVzTiuizsHc5qxu7Io1Y5vcgjXxKnAAnWVTUG6ywZqaAwAEMTHA0C+LsF5t3dvxhZ0HcfbaHRgwiWxxyTzPfmVZXF9Jienl5SIwT3x6OZZPF/cijNbwtLjXS898GsuWPoeJE8OT5heefq/zwUfGSornej7fulc8s+KE694O5Cas1o8Fv2J7bX0dOgfUsE0iRIgQIcJJgoiM5QAhBGfqM1DHTKXBLVRxU4UorwjZUkDLGujvdBLIk0XFqBw/ESXVtQAhICyoOn37/Qvwu+sXI1mTBAiBdnoVjEnB/K0ek1DctHK666TECSZNMjaYdQblP5gVl1OoQ34AQDftNQ707MS+fT8GAMjQQQjBc4tn4sKGcmfdaSX4xntPBeB4V2WGRIJ7W5tL8QEB5wSTSlrQmHDaBVl4x8s7Mf65TdjU0ovv/8Np+dOTDibb+4nPBiyBJIlrL8lKWLfoK9g99fKAykSogXXyHmQVkY8l0ST+1iFaT/21Xfwfj1Vh8uTPAADKys7A2We9jEUL70ciMc66Oc7+CMG8BpMUSwRXnOY47IvjiXtfUDAZyeREAEB9/TWYZuapWYjFnPeF+L56zBfatBxlk7Hhelq6zsEk1lZ/zoMNK7CvUVTyNnfnLqCIECFChAgnHhEZywkxwF6iLsCV2cWW/6i5RAx8Uxcvzbn1QE8W7U3eBP6qCZMgyTJAAcKDg2wyKeO8WTXQ2PBhpcc7etGl6vjsBdMDy6xcsZf3dgWWxQu8qsmjpov7TmMcmpp/Zc9/5tmpmCz3gBCCzMpxyKwQpq5f3nfYs31JkTXIO0yVgNhVjQDw9aXf85javv7IXiSeOox713ktOfb0DOLJzj7PPM1nfPoj8iWcMvt5EGJg4d4YBgrrAK5CId71KGHYJrdg1ikvinOiMjLmPf3yLqeKsrxMFEHU1V4BSUqitPR0e5m8z/vs4mY3hRgl+NCySZ5lJORbdMqs72LixBtzNwj3bcT9OYjm+SYU7/ZqjgbuxA7Rmrlo09+DA40iFD5c3luECBEiRDjxiMhYLph3RgJFNS/x9NW2wpSUht++Oec0oKZRJNK72/dIigJD1wBCwDNlge0yhhM2HA770yres2mPx/UdAJ7s7MPCSaaa5VpWVRRD2ZQSSNTXz3CYY3R3r8G7astFm6S4SQh8if2TJ4iE/CrmhDClhAzDiGHVS+9Hc9M8TCg6DGliEYwqbwXjnzd4rSW+8dgefOS+jfY9aGs54rG1sFBY2Iezl/8RMYVAG3gYaupuSDTu8d1qnLwJACDLguBkDQZoDKQnC9V1b8vLz8CZZ/wD9fXXBI4T8xngtppebZrGsHCSVxGVpPA7SQgBzxHS9itjnHmVMasQ1J0XCAB3rtoHxoM5ebYyRoNqrd6xJzAvQoQIESKcPIjIWA74iQ7xTJtO+znIGKUEc5aLUFaq28mFkmQZhi7CgJQpaGubgn/L/gxnlor8sZd6RBWilkfC9bbBDBjnuO2a06CeJgbg67bsR7dJuLKuary0aoBIBNTnfzVumCbajGVQ7O+tGfe1BzIJwEzDCdslzxPTnEvgICCEo0im0GcGc9/cICkN8sFB9KsiXLl35wtQTWXsopdWBdzwM5XFYLrwE4Mcw7KznHws4uuW8FBvEZRNXYiv6wRt94ZDCwunBZ41AFCf1cjscd4k/tuuOtWejsdzJ9bnC78ytrhYVNt+ZFkjrpxfjwWzRSeHHz6xE034YWB7m4wR6gnvVvRzqANBlTRChAgRIpw8iMhYDlBfeGmAOlYUlI1MxpJFQtVR084gK5QxHSAit4dzgsVsHb4xTfiDff9AKwzOYeRZ/bY/ncW5s2vB6hwfq9+1doMQoN+sTuScY0gzQCQaIGPv40JBKuJBP7R4vA6p9oe9M33Ny6lJSqnrNaosdikzpoJTQOmw1h1ufH7tnwAAXYM/QR/KgIyBF4Ymo3h3F0p4r72emnSumcrBPo4e41W5ElK3SGKPbezG+aveQMrMuzvSl0bjfz6G15q9vl3cNHz9+DlTAAALJpZ7ll+92CnuGK6pexhEdaP3WfibmHerQikbX16An7x3ASa7jGef3udc+9y5PwdQ4QpTAtwVAp3YyZEZinLGIkSIEOFkRkTGcsCfFN6luJKvRwhTEolANlWkfZs6sOfVduzb1CGUMU0DuMitAoBEYggJl41FlvGAMra8PNyE9dZ9rUj5emQ+2N6LopiM/rQYzNtTWXAuQnVxX59ChQllTEJYlR5Dz5G7fBdGbHsFVqrY5I66wmZUliCbhQFKTKhQXx1veMKmw+GFF4U1R0ytw83kB6CD4ty0/VmPYS1BG6aXLMZl4z8OrSioujU0ODYayYyX+Oz72wF8esNeAMCFt4u8snf9zxrPOkaHOPcvX3oKAKBgmER6miNMCSDQd/Kl7hTGPb8Z24e890OWnWfclM5i74B4NjGzR2ncZX3yyl7nPshSEQgkVwI/AScUnGfBWQaUAcg6JDZChAgRIpx8iMhYDgSIljtnzFSE6qbNCN9WInYe0YbHD+Afv96KJ+7YAiorYLponE1BUFcnCEHzXsf4M8tYIIH/yhqvKmPh0Y5eDIYkdBclZNy15gDO+8HzdsViijFUw+uHBeOgeT3BfXDOPAaxO88W1gvqGdX49OWzoJ5RDQqGtrYpMFxO94QSXK4uBCAc9AGgseenuDgRzFvSG4Mkkw4Z4JyDs2ogYyC2odNe1kWq7dAllYHTK89HkVKGYgRtQuw+lQC2+VQvAPj7QWHEeuFsxwvOYK7m3z1eO4jCYUKRmRxJ9YBodwQAs08RNh+PmUUK6wcYli19DgAwY/rXPNvsHMyA9ggypph5elmX75jbb0xWSsBBbWVMojI4kZDtvRPZvv8BZYCi5u6xGSFChAgRTjwiMpYDnPoHWJf6wxnmnnchlHgCAZAkKCUB01gAMDQCQ9fBVcOjJvV3/d2eVhkPJPC/f1wFZhWGHMtc3w+LOOzvHHT6UtYlUQxvWx/JED0TJ6IpsA/GVBTBcdIvVUwCIFMsn1cHEAIJDC0H50B1K2sSgQJTPTPE/11dz6El7ezLGJdEPCZBn1mK7BLHy8yCpg+CcRUk7Wsr1J7GYYictOricc49kINhuOpq55o6Qtz9aWsaf1jbhL9sdLoCpDKCfIY1/y4KIWO/uW4RACCdyu3jZRiCVFk+Zpp5LgohSCYnYuX5ezFhwoc82xzuHILcLK7JUsYyLlPc4pjzzIsKZwKcorq6CcUl7Tir+iIzTGmGqQmg60EyGiFChAgRTh6cUDJGCPktIaSdELL1RJ5HGFRZxbqOJ5wZxD3JwRn35Ix9/r6/Yfn7P4xY8TWgEkFBSVgek9kc2jBAXTt0G7FmGYPGOT5UX2nPO3z4TzirTKhI145z5lvr+7Gn3SE+j70u7Ch4gQwJ3pBmOXrwm1PqcBN+ENjHUPoAStCPr/Cv47HThYXG9AJREZlhVkiMgXMKBrcnF+xr4y7CKbuOrc0rx8r3ivAfL3eqLFmxAg5g3ZYvg/F+EN+lxTZ223YXuuQk4muKQzILCqZ5tmnFODz37IHA9cmHhnDzX7yvncWB/3gk2L4oTBm7YHYtps2qhBHilm9fExOhYVkWOV9pyz9smNDm3jZHybLIWF2Fk7OY0pxtJSkBEAmEcMyf/w8AwKH6c+zll67naGPBpvZhUFUVQ0NBIhohQoQIEY4tTrQydheAi0/wOYSCUAlNA85g7a7CIxBhPEq9eUQLL30nqFQBQgnKagpQXOlVs6gkBnSpKo7dUqs9303GVC6UMcWVR7Zz5y0oMisb6xMKWs+bby8bcoXIlJC8LCuRH5SE5oZdVJlAAsGqyv37fwIAmIOtWGhWe35pslCjLDWOggVtFtxtnFxVjVfgIWTProU6rxwgBA+1OWqNtZZRlwQBsLN9K3pqOiC/EVR02jNCSTPkNF6Wd+I3iWdgFDghyUUL7/Wsv7p9hT1t+aXlQrfZtYDml94GAChJKuAqg+56DlaXAcBNxoQylsnqkHf2eUx5/WhnDrmj5jMtrneFYjm3w7UAUFjoJPenoWLflCvsz/OaOEh+9SD41a9+hdtuuy2/lSNEiBAhwpjhhJIxzvmLAIIyxEkAQgmYK5eKpryDJ+c8kFfGLJJi5vksvmyyb59m+E430Eud0JrsIklZxqFzQPIRK5ln7eVuPNbhNUoFENpCCYCtjLW3N7rOOXfzaT8sgpi1lTEDnFHRB9ICJYhx2Zx07t8U7AEvlMHqvQ3SAUCfUwauUFQlBan6U/oD+G92C2ja7MFZs85e946eTwAADsYO4w1ZeJWxSpEXp0PCfjUJpjo5dvHS9zgHilFkVjrhzVxIUArEKc6fVeOZ/8Snl+PFL5znmVdVEgcBcOeeVvu+fHpHM8a/sBkAYBheZaxpexfkAwO4x2d668ajrQ4JtcKjXa72VqAEQyjAc1iJHYNpSJJDzIZIkFhnkN8z7uzsHHmlCBEiRIgw5jjRythJC2KqXkf0YEsfAOCMgUheZcwmYyZpkX2WB72tgjzs634dEneWuWlXljHojAdUrkzqNXu5G/e1Olz2vAqhvvj9wCxYZIy7js39bXiGgUUQtw1kzPPm4JyiijseXIQSxKHgE5OuQtJFVuXQik3gWv5bGOMLkT1/HObERK/LPWvHIdbkhB6vzqx19m/eY0l21MT2rCAs6+rvxznrduBQepG9LJF01Mld55wqTGxzwApTZhkDAUFNsdeo9pRxJZhY6SWT8+oEyfrOxiZMeuF1PNbRi4debkb8BaF8Wu2VrFZI3BAH2dHv9Tvb0z6AviHzWZjC2L+dP9V24D+12HVcStCMSfgN+SRWrNvpcfmnIODcS8gyPOpNGSFChAgnM056MkYIuZEQsoEQsqGjo2PkDcbuuACArep6VH10bmA5ZyygjFkDraWMyT47hN42kSy+4fGH8LaaM6HrjsP8Ur4KgAg7apyjs83r8ZUwyaGljK0o95qQAsD8EnPAVsLjbGGEKNCGZxhYBPH7BwTR6EANOKeYwKoASkAqFXS3imvUdvYiu+Nye9tckb9L8JhtFXJ56d/s+X0HXV5a6SzOnyOqHpU3enEn/xSorKOi4iBmzlwFxTSv3aOKUF4zdcKRu1OC9HAKlJih3uzSanu5URm3uwNY+p7GOcA44sMQNwuXThZh09imboBx3LL7EJRd/SAZA4xznHbqrzFv7i8gSUFF0N3+6YLbX8Bp33oSqs4w3iyWuP4Mp+3Se2q9FbWP4F3ONRhOnpcBDm3gUfszB5DOQYRzwTBy58BFiBAhQoSxx0lPxjjnv+KcL+KcL6qurh55gzGClZyvcx2J6UFrCUM3cHCHN6fJMKyWNIJ6UF/7oKF+MdynOjtABoagqo5q8w48AEDYGnAAWqYZc5IaphChzBXGhAJjKWO3zRR+XPVxh9C9q7YcFAD3kcDz5wkiYyljlDiDbTabX3I3EOiGBA5iq2wN31yKezd8G3//n9vt5UZvI9rapuTc34385wAcotZzyBXWdRGhL2s34L/f4zjev0jPR3xCF+bMfR41tfsRi6VhGBKMfh3Kpi5klCQGtAL856pbsHavUA6z5wmF6uKqEnx3kXNO+qxSsGrxHJjZAF5lokAjlgcZm1LqkMbEU4dR1OcojWmdIZmcgJoaJy3SMCmf1JnBzduDqutz+zvRvlH86EgqTtGAp0sA52jEPvvjlX3fwmEI4+A+vQtMP2IvG4orSOcZpiTEgCSpePbZZ/NaP0KECBEijA1OejJ2omARKUMLbxnU0dyPtX894JnH7ZwxcVv9alDalXfWdbjFEy4shlBJbt4tlCUJOu5ubMW32GfEZzOcWGjue2IyjjgltpP868vmoDEZx40TqhEvjuHK+U6LorPM3Ccrgb+za6K9bPuOm3PeAz/8odNp2AXGzGswCag7z45wYNfOs+B/zSq5IBvj4G083tveYE/zAWc/n3vHWSh0dffVngAAIABJREFUtWaS9/RDh/O5vmEnOKdY9be9kNoyaOoqx87uaegYqobUKpSxX57aCAC4a94UfLjBsdPgLoYZVMZyG73a1+i7JwPNTiXkoOZVmBjn2Dso3ifao2Jwo8jRMlx5gO26br97hb5wc/asGnCJgKQNlKtiWzKkI/HMEfy55Z3i3JkGEIplNe/AynHXwpBLYCA/pWv+giew7Kz7sGnTprzWjxAhQoQIY4MTbW3xJwAvA5hJCGkhhHz0RJ6PG1bO2GDP4dDlmhp0lVfNhHMqi/mST1mR4qfZ05wzDxkr8XmAyTAgEWITuguLuvGpiTX44mQnAb1ElpAy1biYSYaSlCIDjh9fMx91ZpNpq3eiBANbt56Hzo5G55zV/EO/snm9jUmRML4Ar4lrkAiISRK5yyPNKlIgRIQBb+Ffxef5d21fs5hZxflv+Blq+RFQxr1GsHGCT5M7ce2Zk5CgFPpUEZqV96bQpXobYsuyo/5kdAU681pRvLM22EBbbOjOn7O2ZwBHXsqYHzEXgUqp3vDgk539gOHcH61XXH9HyiH867Z3oGx8EWKFCmSf/QUvUsAqYiAqw19fWgkAIGaHgpZWEZoVrxTBhMKZqEo0AJA9z2Q4FBUJpXdwMGqfFCFChAjHEye6mvJ9nPNxnHOFcz6ec/6/J/J83HDng6npoPeSoemAL/m985BQRarGC9JQ0eB1hqdyvesTw/79p9uf/CoahQG4WjIpyODmyTWIGU7T51KXchMzzzdh/q9yDmYOwgmTIMhm9aMbuh6sxvSjr28TDCMN2SR8gwZDGbdCtAREcc6Du5SxLjJgHkN8noXtOB2v4gb8Ap+vPoxJOAAAOAsv4Xb8O+r0Slw24KgyVOYonijIp0wJZs1wPNa6sl5yta1/pj2d1iXs6pk64nUBAJQgGetsE2TEbQg7LFzq2lDKeScGNS8Z69MNEMPbrQAAfvjkTnveo+ta0N2UCoS4HZiKrWmoa500oaaVBoDTys92n5y32jUvjHb9CBEiRIjwZhCFKXPAbej6s+uvBpG8A5SWUUGoyCVb/v6boKZ16KqpUiUFOUkW+Y1fXSExztHbU49cEPldzvqMZbF7z3exavVSaJogUCVuMmaqVnHbfoLblXiSmUMmQQfnYrq7O/ex/djw6lXYtv2LtjLWoeoezzLiqhp1D/yyGUrUdS+xKEU/ri4+GCCgh0k/GlMpJCqsBuQMpTVOfte/zXRUwW7Vm8f3w1c+ZU+nszKeb1luf77h0mDbKn1qMYxaM9+LWCFW4NrX92HTEXF/x5cnA9uFIebyk3O3svKHKQc1HdJhl1+dedz7X20J7FPOocpJHU5/0diqNkgt4odCjIqKyU55CNOKnfw6TiQgxBh4OMhyVH0ZIUKECMcTERnLAeKrlKyIeZstc66C0CQS5Z/D+idk/OPXW8F0Mei5w5O1k0tcW7n3OfwAKcPwVDoypqK7+yUAgGrmC7mVMUu1irm8wH72vgW4YflkfGKvSBSXYNg5Xk0HHOPYfNDe/rhNxgDRJ9KG22YMXpsFce7B10w3KwB37VxqK1IJI4mrsmciSQQZ0AcpKuschevy6jLMubgRANCnOl5qmi8kub/F67OWjAXd8999diO0+V51TeMcT3f124/mJ+9dENguDA9/5AxU1IpqSc3lxj/oc+bfs9/7DqlDuRPr4yHOsy8smeX5TAd1m5xRUxlrLjngIcSMyqg67LXRGAlTpm4Y1foRIkSIEOHNISJjORDIs8kqvhW86kHztm4YuuWB5dzWhpluBcfVAmkEtwEJOrjLkLW3dz0kSSg1hiHCaKUhCeZWmDLLOE6bUIabL5ttKz8KNDtPjfHRP/pEDit35urN6CYCVsbbnt1nBrYZHDTtMTomwbov52ZPRQHicIuQNTVOhWVCovjfhYKcrdlyuu3+35cN2ny40VgZbCT+41Mm4i8LROukAjMk2G+FFU1SXZLI3RzcjdllhbjlYkGUdDcZ07yEe+ter78xNzg2HwkPE3d1BgnUzBz9SQEnTBmLpT3PwKAU+sh1CB7EY1FLpAgRIkQ4nojIWA7Ekt4QFfG1/aFKY2Ab29rCle+z5O2TceknrbCRM59wjmlG7vY8EgwYhjMgd/esRiolTFF1k4xZYcpTXIO0paiENRCnMGwS5s8dyyfHO05G9qvq1xwXd6uysrd3XCAs2tHxgHlcil27liKbTSLGLJNVkzAmJdTXeq0xaoscI9ZPPvN97O+biAf3XWnP0yc4xEtvLII6vwLvmu510rewtKwIj50+HZdWlwEAWrOC/BKDg1MEEuiHQ6GpvnEXAXPnjLVmNWw5EGzv9PLhkXP28oGdXkg4wDkGkUGKpMGoBFkbnW9YWXnryCtFiBAhQoQxQ0TGciCW9KoQCnflZ5V8BHJyuX8TJ0zpSgqXJIrJp1ah8dQqjw0CAwPJaYUqlDGDhSsUlsmnZTXR4xpsY7YyFgyDGpBtEkZ8Kteqlz6IQy1C3dm+7ZzAtgCQ9JGxg81zQgnlTmwEAE8DcT/5s+dziva2qVi39t3Q9AyePHQXrLinPq0E5cVlnvUJISAm2dVYDN9e+/+w7pAohNBmlkKf7axv1CTAaofP+1pYWmh/CVb3mlWEBgdGQcQAoNAqYnCRsS89ucOevu71fVAnFfk3s+1QtJklnvlXrGgc1fEtZYwShteUA/hTYjXui68RZCw7upwxAEilUmhraxv1dhEiRIgQYfSIyFgOEOK9NUvgOKgTWhhYDgBrH9kPwDF9dWPibG9+Eucs0MD5+hpXBSfidl9DPwxdkIZnuoUdRqvqhDMT5rEHjDAyRu0wpa77iwuAffsW4eU1V6OzcxLKy/4LHe2TPMsTLjL2Xn43OAhO0xtReqm3B+eeg6KXpJuMMZ4rVubcq7TWhx61DfUNfTCqEzil8GDAxwsA1GnhYUnDtMXgprUIT8qoUPKI0dmHMCsTDWbvI18UmkUSxGVdYXmcAUC7qgMm8Xr8JqfaUbOek0KRPcPJw4sl8wuRWiCSUASLIGOb4tixMCJB0kZPxn784x/jl7/85ai3ixAhQoQIo0dExnJAkryD4ScRQ0WiG9dOewi5m/sIhBGIWUvNSkAiBs0wZew/xzuD5hAKwIxcypggY9WKk8fW378FADDB9ABryQQr4qa7TFpVtQCSdLZvDQJdF2FAWZ6LrOpt4dPV9Ty+OkVcxyV4DOAEFATUl1tl5Sy5DWCbm+aFXosbNYkJAIDCeBba6ZWYoYX3BTUmBBUmALiwsgSPnT4d2pxysGIFiFOsXzp7xONaz8FWEw3YJrb5osht7+GuLjXjvxIRfTU5AWbXl0JvEPc2nRUEtywmg5c4z/Oy8Y6Nhxsza8OJqBITCmWcwvNeMSpBUfMjYwwUOsSzjFoiRYgQIcLxQ0TGcoDDq6jEIOGa5EbEj9RiJDIWBiUuoWZSMRLFImmcc4YmqQN7di/B0JAIUe3dexueXCRsGOZhsydnzA2rhdGPT5lgz1u/4R0AgBKzefmAazAtkigu5o+Cmo29LRB4qw7dOHLkCODLk2s59Af8+6RaHDr3VMjQwCHIWKBPknl/FutOJeTQUBlGQtZU/KhuhSFzJKyHeHDpc8vw+3mTsbC0EKwuCXVZDUAICqWRlTFrb1lL1WL8KMiYQ0iVRND4lQ/pkPcP2Pu93OyQ0J8RyysTiueYEyvCw6ssR3IfY2JbQgwQAIQwEMJgUAo5T2Xsv/E1fIjcl9e6JzN0xvHHw10w8jS7jRAhQoQTjYiM5YQEpegq+xMFQTpdAsOI4WjIGACU1RaguPoiTF6wCBJVkCEajhyZid27RLVhb+9azC1U8EjR1zAeLWg5dHfofgYGtgMApiTjgWVFZlL/gO4MwBrnUExfMDcZU81BurNzAvx4+eWXwf3XafZupFZ8lRNR2OAb8zLGAGhZDDPqp+J8zWqyHrxnBw/O8Xxe3/E4AID1CuKW7g0vcPiPicGEfG5wW5F8/7gcbvsjwGrCnm+TcDcKXf1AYy4rjVbTXb9vrci/ssKYy6sEAe9NixDznoyKRxZMs9szTSgJJ2OXzBsXOt/ikfVznwQBwcJFf8XZy/8ARigkneO5ne3Y2zEw7DVsI0K97D58CqZMWY+Fi/467PpvBpxz/Nfew9g+MDrbjXzwxyNd+NzOg/htS+fIK0eIECHCSYCIjOVAQRkBoY5yRD1kQkzPXp6/cSogEvuZQVE3dTrmlC2z57sJkttbLBeoaXFBCMFfF0zB7fyT9jKrd6WljB1IZ02SYYYOXYn0zc1WblG4gsB9ylhq4A2oaie4Sco4JyAg6NrXjK4WJ6RocB3l/z4biRnlmGLUQsqhTnV3NWCJNs0ujtANQVyW7t+Pqe0tOOtgeCuqxhASalQ7Kpp11tfVh4f6/KDUG6YkjGNBWdAOYzgkXGHKFHXu58OHRMcE3ec5VmCSvcdeMe8bBZaUFeGpm5bjJ+9fgFiOAoLPrJweOt9gzrMqKzuCZFIQL0YlgHN8+HfrsfKHL+R1LQNSEg3jd6CgoH/klY8S3ZqBXzS3492b9o75vofMPLyDIaH6CBEiRDgZEZGxHKAyhUScAdmdh2MpMNIoK+5kmULXWcBQljFXvhHXbbKTC21tjyCV2gYAWFwSRy2cqjeJECQptRP4P729GQCwBzPM/buOZR6X5vAPk6WgKenQ0AFYrqgcgqRuffofuOvzn/Csxw2nd6ebjKmqO/RIMM2ow9vVRVioTbGJ6IReFe9/YxdmsPDQ5pyiJNR5Xgd+uBLe06bCNa0gSNrCYD3ZjMFQF1MwvzCJZD6J/y7IlDhRXVfy/09XiaIO4qto9O9/xThxPTNqi3HlqblJPqUEsxvLA/Pdr8yMuU/b00MFNSAhNifDoaP22P9ZsNIqj0UoUbI7KkRhyggRIrw1EJGxHJCoAk4VgIhk8d39rwEACrkzwIcUVA6/z5gEQ2OgVELL4C57vlsZY0zNSx1bv+Gd5rbBROsimWLQDFNaifxZqQqpVKX3WOY0oeHkrz9VFZj36mvXOMc0lbEwaNksug+LNj8WGVv7ylXYsP5K23OMcwIKigpehAXGZDBugMgNaEodwvR2HUNl4WG1+SUFmFR3COr8CmRWjkNmpTd0lzaJaHGIKe5wyDCOuMHwekvfaFPGhOWGOfaTlPP85IODoY264z4if/mU4L3OhUsvmByYd/hAChs7RZjRHV7uqFkAkgfhcZ/jY3B82zo68m8kfzQ4FnTJImH0KNMJIkSIEOF4IyJjOWA1CpcTCwEA23rX4O3Zhbgyu9heh4SM2FU5Kv0AQFYoDI0BhGBH31p7vjt0mI8y5qxngLEgcSuSqB2mLDAH/eXyG9B1bxeBykoRIisvPxJ6DGaE2ytYPmdWAn9Y9eia+/+ArtdECIqap6iqBTCMGPbsPgNG+nykUpWeAZOBgcoNkApWYkvPi1hy1YU5r7+Ip4WHmEwBmeIHM528N5uM5ZG8D7gS+BlD2+NCSXxu59GTEJryKoq/aG4PrBPzFSHEQ+5hLpxXXRI6/+ev3YDB3jpP4QUBz4vxMJcvneEqXrE6JYw1LEVs9E3MR0ZaNSDv7IM2SrPbCBEiRDhRiMhYDhDT2kKKn4542WfAaQK1vAwFcJSxwlJvGGzc1FJc+Znc/QwlmYJz4WHGXITL7cHFmI5MZtCzXVur14XeQjrd4lHRnnl2Kvr6XkORJNlhyqvrRDL7xfJ6WLSj3hBhrnh8+LY37vCpG7qeEhOmtYVq5nq50d/ZjgJJkAaiegfcbLYIrQeXAaAeMmZwHVSuB5WrMX+gA3VTw/OjAGCLdKrnc40raX6IjU4ZoyYRyupjM3j7PcrW7+0KrKO4QtWsQLLNevNBoyv8evW5k0FdxQYcxJPrR8E9ytj9G8LtQhhzrj3NHEsTTQsn6m8WrlqJMcf23V2QDwzg9Y1RJ4EIESK8NRCRsRygpcLPiRAiDF59yeyV44tQXucMWp/85Xl41xcWIlHo62HpguXMzwwO7vLg4h5lTIWmec1ed+0SxMUPxjJgzEuEmpr/F4USxYBJLCwFQuGaPUgnEUeCK4EE/eD+HYJzxpLH7WnLcoNDhCn3pjbay5SEKC6gkgyDC4WohAUrA/e1Non13MoYKYCkCOL5l0vC1Z9cOJR11Kgu006iKqRB+LD7GAiSyqPBdz+8EOoCp6LzhSf329P33SgqZxWXMqbPLIU+itwpd4hzQlWB3fkBEJYW3NN3lHl6Xd27PpyMbT7s5JkdktzVtccm78pRxsYeT3eIFlPMiHLGIkSI8NZARMZyoKDI68Fl+IhLeV2Bx2nfHarjhiES2H0wTCuJof6sJxTpVqAY1xEcogiAYOhy565vBrzIOjr+jiJZsivKVMt0lKseQpkhGo4cnhHYpxtusqYoZa75phpnKmPuUNPMpaJNlByL2erf+Vpuw1cCgiFdVO1xYxBT9j2Cs9Z8BW875R3DnltwPw5mFYkigckhVZfDbUy0sRm8PzC1FqzGIaAFpoJKkhLOmCIqPN3VkrxI8fjCjQTZpaJNUHzkn4iMqYf3XIK7t10NSrydHvQcUtTl+7xFAw/iPfg2vonD+1vyPq/RQDPfy1y+aUeLlG4go5vv/GgT/yJEiBDhBCEiYzlQXuhNqPZ7bnEGu0eiHwfe+z7sXLgoML9pqwhX7d/UDg5HMfJYWzANJIR4haG3dy0YC/o0FVKCfnNw1xkXPSyJU1tmkaeu7vHm8cOvQ1UdQiHLzv1gTLW38yfwN54m+kRKkmwfJwEFE43wBHUCgmcO34NX2h8Fg4qYlkJc7cO8ORcNe+1+uB/FT2dNxPNLZtr5ciPBUqVon2OFcP2yxlEdHwhWSFoYMEnpo586y55nnS6nAC+Qh+1TOhwMn/pzZKgKnBM8uu8SPN9yNqiheaop5TwIyjn6s3iIvBfbyVxs3//aUZ3XSPg/0/Ij/SbilBdt2IkV63YEF5jPc1Nq7D3MIkSIcOxh6Axa9l8r53N0cZx/IRQkvW1nWMAAlYf2oASAzBbRmsjo7YVU5ihK8QJxuwd60kiaQT4gmMAfaFo5DCxi5EZNjOJgRgXjHCrnUCgRSpxJunSIl9yytvA3DbevI1OMN7augK7HkR56AkkzKst40PLCgmQqNZwzj1oo5eD9jx38FYaMFJoGt0FOrgC4sOxoqJwUur6FAona6h8AXFjpKJmFsoRZ8vANwt1IW8nrZtugx29ajtn1owuTAsDq/zwfaTNpfO2Zp+DMPhXxVzpA+8X9mlvlvFMVyRiMcUnoE0XBxzV1R2dUe/lp4/D5+zfbn3enJmF8WZP92V/xq+T4AeGGRJw/gtqkcK+3N4tD2TfvAbbZRbY0Q3xDDe4qWDhGwtgdL+zFrU/swM5vX4z4KCt2I0SIMDIe/PZqdLRq6PzQS2gsacSH5nwodL1/bNiGZCKOc+ZODV3+VkKkjOUAob4/ssTXf5GHNwR3o/v3v/d8TpaIvpFEKgfnzJUv5bW2AIK/CAgaQo/BQmwwahThyF7//GbccbADQwYDYxkYZg7YmbrlOTby4+/unoD+/hps2LABc+f+TGzHLDf/4PVTU43inIO6rivBw3Pp3OdP5QmgTBCXmD/85sNrS2fjmcUz7c918eHXHw69JoGy3PGn1+auiB0OFYUxNJQJEjgpGcdDZ+QOA0sSgXZqBXiZeCeUowyp+cmARHUkEq7CDM49ythrTb3h+3n+CBL/OAQyqKOHOj5mSiy8Wf2bRV3s6J8XAHSoGsiQDjIo3p/pNz+Bxd95GqrBoew2zWqPERm79Qmhxg39i/1yjxDheKGjVYwDDbfdh70/vQ1P/GAydtz7RXt5f9NmDH2rHhf9bSnOeeD0E3WaY4qIjOUJ4utVyRgPDVOqLU6ODYnFPMvOvHKKtQAcLNQHSdf7EZ7WHPSWAkRY048ECclXMwZhGDJWFp6OEp40r2GUj98kX1bOGAcBk7znSk0SyxkThQ8mlujTQnfpbiYOIqOqayt+dOXI51WmyJhTlMRzi2fi3tPCq03zhX23mAis5hPKywfTywtyLjvasGQY4qXOe9ZLff1GXf5nAKAaDD2DQVXKMqVVNnZhExba87tR4am0HCucUuSY/+4ZEoSPc+40ax8B81a/gfhLbYivcgyPe4Y0DGkOuSdDhl3Iciyw/cix61AQIcK/Kg686KQeLNsOvO8Fhq8XF+I92Sew4+/fw4G7bsCaP1+MMyZV4qflpTgkS8j8E9jYRGRsGMza8jkQZg0UotJud78IQappPVQZ673/AXuaxLwJ5DHTJZ7KjRjU+3CmFlROVLULYcqY5Zy/d+8izJxxj2t+UBlLdT4WmKfrXVDVAqDHGYhzKWMxHh69tpQwxs19cAJqeO9B2jQ87WtvA3URWCUkIr5cO8VTyECIhLtWqnh5dv6v5SlFSayoGH1I0Q3dIgAGB6Rw37SjQVUilnOZu+jhJ7MmjnrfXCEwqsT7ddpFDlF/o3+mN6ROWcA+YiCb21SYDuogQ87791PyBRjGyCbEo4XBAelACmRIx6GM+EHx3X1HMOmF122fuHzhNqzVXGROakujXR37c7fwwGvHprghQoR/VWx6cCMe+6OTGqHL4gftOVvFd/w9bffg7eQVfKFG5CD/uqwUF09owPamI/j7lhYc6BwM7vQtgoiMDYP6riziWeGpxY023Lf/e3itS1g8pFMqqKmMUZdCRlzhNVrgzVuyyBshBFSZDMKdX9Yvr7kaANDa+nCo6WtXlyjXJ+CIxx2VibFgGCnT/0ro9Ri6YocOa1iJrYxpmo80jkDGrDBlGQuG857+nfhV09XSPKKhZylLepUxyBhMAEvTxzfxusIKmTGOUVvvHyUKzIrI6QVxXHMUjc2z59dDO11UZp5S7LxnLW11uBsfdq1pQJO9+XfqCGTHz9GNkC4PbxaptAZlZz+UDZ12ReUfjoik/sFRkjHdo/z5PO3yVNqOBsaxMEmLEOFfFP1daax+qgcAYGj7oWdeg6YIMvbRp4b/Hi+4Zw4ufnAOGn9ej7T61lTJIjI2Amrbg9VkclzCGVdOsX2MCkocBaTz5z+3p1naS5S8SprkCf/ouiBESqwChDC7ZZCFoSGhHhBqQNd113apwPklEZ7nw0HsRPpxrBwAxe7dZ2DTxos9601k4ZWP1rimG6JNUTEPSZJ3hSZXtT0UWFzJ3IURxGN+W9OxGSvUIVw24fbQ4x8rXFwlQnvE4CiOjW1CNisI31+hLOH1ZXPw3OJZR79zU8H7ylRvO6jnt5zhrEIZ4AszZrXh/7AlmNcMWBuF7Ua+sM6AaCzP2mEfXNegugjX5mZvTtyX1u87mr3nBUWO/nxGiDBWaNvTbU9rA3+Bnn4eh1wWQTMPOj9+vrPsVmz50BYUUpHu8NPyUny4rgatkoTbf/hfx++kxxDRX5MRMGX/o3j7Uq+D+g0/OgdTF9QglhAK0rwV40O37X3gAc9nT/skIgdycSSpErJUBEI4BlKVnmWWSz+lzEPG9h/4H2eXRKxTiCBBA6xekOIcJhs1AIDWIzOQyXjDfEv0abjpyhtw1llnBbYHgP37fyqOp4Q5+DvXOKD3YOvEDSCm2e31mRW4Ql2EOrMBOCPMowI2Nj+FdOUSXHnZFaHnf6xgPxbGURIf2wJjboaml10erPapiStHnZ92XX0lvjpFkLA4pR6TWXrEZV5LdBjEGy5N+/IrDN97qHKvUmrk0St1tLAbhHPhNTaoG+g2zyufFkm0x7nGJ7Y4XQK+cu9mz3qv7Q52P3izsDosTBxXPMKaESJEyBcDO/cH5tUtdv72/Nc9Bv5wdz0eOfs+XDH9MnDGML9qLgARrtyQTODCiQ14V/rP0Eeprp8MiMjYCCDg2Lr+z9555vhZVluA6767DAveFp7zIxXn/mNNIHn6AZpbgHEVhAQrFa2QIiVeZSydPmBPj2/4IAAgiRxhPk5ArebgvgTy0/RJuCK7CB/LrIQMCUklDn2/l9T1p0Q8PpsVbWaIFDZIe1+pgZ5u2wRMhgQJFKfqkwAuVDIGA7Hi90EuuACKnoVcUBh+7scQVo5YEQiKcniFHS1q51dBm12G62eNG3nlUeC2mRPw75Nq7c/fOmsajJoEWJGPTLJDMEjCM8sv46v+IpAB7/JMduwT1TXdJFOmE8WNbzh2HPlE/2IbnV/RrzWHV4gCgNQU3mz+TcEk0Lc/un3s9x0hwr8gtKyB1avT0NKroQ063UBe7fwsam/9nv1ZaWlG5rKr0PmrX2PH7Dm4Rgv6eQ4WdGL15p3H5bzHEhEZywOTn96KRMl8+7M7wbu4IhGa8C1VVIBlh2uvIyFm+BQIox2trQ8DEMn1nH0dGzdeIj4zSxkTZKy4eG5gj7Iiwm1V6PTM/9i4AnufVpiS+h79Yn0aarhTicc5oPsGslc3+EK2nKD3FL8K591vf0c7iC+cM5FV4WPZlYhD5GoRqQpy/FRIRhZKLH9/sLGC9fSG+tWcxq1HC71AgTGhEOXKsbX0e3dtOSATEF8IkpA+HI7XeOa5k9w39A3iwcNe9UjePwCoBqQDAwDn2LL1m2N+vpphEUAOxoHX+p3E29G0hgKAvUPD2G8cixTAKFcsQoQxRdv2I2B6M4zMWhjq6/Z8g8vITpgTWL/jdpHKUn+nKFZbWLsQxTEhfjxRWIB9D30dQ8eweOdYICJjeaKoKMjAh4PR3Y3s9uAv51PPM0OaREJdsjHn9pwT6HoNBlIif4tZihZlMAwD4+reGbYRACAGFa3nOeTxgnLLiJW47DRGGFA4D1hv+IU8wgG9wPfC+4jpQE93zk4FDgQBkgwVCZJnC6MxhDsRe6xNPC1D2bJjbA5aKkvgEg2QsR+UXIzf1b3NM4+Z1/vK2m/j8td24//tavcur0pA2dIDZWcf5B192DUw9uSjxzTCFcoY97w2xghkzN/S6XAmtwkxq0nkXHY04Jx7KgbaU8dN812gAAAgAElEQVTGhy1ChH8lNK1vBsLMxLmKh3/bnHM7tnc/Xox9BXddfBfWvG8NAODPJcV4e/wp9PT0HKvTPSbIi4wRQt5LCLnZnJ5ACFk40jb/bODdjnqgtbXnXI8WF6P8gx9E0YoVocuXvXsapi+uhdX84BJ1ARZqQZ8sDgJNc15OvzLW0PABAEAsVu3ZKgxxIgZozp0EfiVHxaQNgwdCmRYZk2WR86UfWmw3PJ+ycAmk+AJPU2px3gwYpi0Rjc3G4te+j/mbfwbKDRjTw/3UjiXcHjVxZWx/n6RMn6uKY6yMEUJQZqQDLUwHaZDcdps+Y6/0CJuWwDOLURCTcMjNg7hfvnRMz3XjoV7c+1czP4SLU6YaA+0QxGak/t79voICLRP8BfzelSJHj3ZmsTkVltt4dMho3l4cS77zTOQ3FiHCm8ShNdshacFcZ841MIPDoF6T6Jr/93mUXCqiRq3f/FZgu/8tLcFQ/9jnix5LjDjyEEJ+DuA8ANeaswYB3HEsT+pkBDUcYrTn3HNzrsdVFSSmoGCR4Ku6j51LEkVlQyFgJts3sApMYtXB/XDqyQ2znDsNXUF7ezsoVUBpDLreZ69SU3MJJk38OCj1JmzHKbf3aYUni5DA9OrGnNeR3tYVIGNd3T3mNRRAVeOAnrQ9ni676QtQCs6D3yONc4bSt+VubSQnFiOR6UFFzw785AqKWCK3UeqxwpArh2qslbFfz23E0rJCVIxx+DMMmZ78FKwvPCDCAL9VPgJ5Ry/izx7xrsA4yIDzvoe5Q8xdtRVv23B0eRlPHnTyvYg4HNLr2hF7rQvQGYwRVFu/ctbaFCRDpQVmCFxlODKMcpYPsrqBfnMff1oX/JX+VvY2ihDhZEBaUyBnmoILTE/Lw+NEMdmke+5G7Ve/isqPfQwNtztV9wMvvIDuu+/Bpg9uAgA8WViAdOqfTxlbxjn/OCD8Ejjn3QByu1n+k4JqI/fS45ybZCyG2DThBTbw7HNQm5qgHjxoryfJ1OPoH+rGzgk2b3Yqw9rbJuPw4RloajoNr78uBlNJKrR7U65Z/V4UFc0EoQoY0zxGmIrVixIEkqswoLzA6ZvpR3pLZyBMaZu+sgw4pyAgsNqPW3lzhHoT8DnjKJhfg/j0XMeiGIxr+PKHJKyeQ6EP0/fyWCF9DJWxy6rL8JcF08fMSHY41M0cnfpGwCE3DQZaoRKD28oYAPSRIEHu1HS8fpSNuP2tnxg4jJQTthzJZ2wwj1yQbNpx8TZCfPtGgw/+Zh1O/caTAIBv/U30TmVJ5/tLKYFusLdkBVeECCcaWlcPUgVlGKAHAsu4ScZYRS1IIoGCRYtQce0H7OW0tBSQZRz8+L+h7TvfweDf/wEAaJdlHOk+Nn11jxXyGXk0IvracAAghFQiEAz55wfNpyWMrotcq1gMUqEgJUduvhl7L7oYey98m02QZIXayhiA0LZIwWpKBXv3nAHDiKG+XniQSVKBa7lVbakA4OAuo86YK0zpTtynJkGYZASVOSCEJJrnpGndoFSEa2wbApuMFUMuuMB1HcycH7zG17qeAkDx7WsMJCrFl25iPNwm5FjCHaZcs6dzmDVPbsjK6HK7aC4Fyhcn7GzNTdqPBjHq/bMzlNGdCDsHbtl9aNjt+zMjfxd7uv5uT79xIHe1ZT5Yd6A7MM9NViVCMO3mJzDt5ife1HEiRPhXxMEXt4LpObpZmD/Oyz9wLWauXxdYXLR8uRh3TRz63OdxXd2FAICeviOB9U9m5EPGfgHgQQDVhJBvAlgF4LZjelYnIfpLRu5/yFVBKEgsBnlcfWC5uv8AAEBSKOBqDxSmjIU14bawbds2bNq0yUPGrPUptZL1HYUpZvaqdFdTAgBVzfBljkFZ8r0e7nNSlCwICAxDXLMkO9dDXY7vFgGNn+71TQOAnmw7CKG4QJuBz531GK7bdy6mnfa2wHrHGu4wZc/Q8VfmxgqUjK56iOR47qTfqwJLh0QYbmhoCB0dHVjdE+5jly8UX0FHU+uAfSa0M4PtA8Mrbtk8TGglV3/WoWHaP40GbrXZ/ZUdazU1QoR/JaQ7+8D01tBllQ1iPNN17uluYyFs3ny1AQDABnIn/p+MGPGvCOf89wC+CuAHAHoAvIdz/qdjfWInG3Q52PrHD2aRMSWG2PiGwHKeFQnKVPIpYyHEK1ffSAsPP/wwJMkdErSqLUUEmbEgGQMnHuJnWVewHIOyzP1kLHhOaiYNOR63G4QD8DQIB+doP7APv/ruDSFH4Ji39Te45NJPYMmc6fjCN3+O0oLjHwH3m6C+VVFWGG4LUqSHW6xQn8AdLxekRer2kjHaJ96lO++8E5+9/yFctWnvmzpP2Rey3TOYcSqBt/RAU4cX3rNmOHB6Y27FTnaRMX+LpKPFq02uHBSX0kuPQwg6QoR/RnDDQPvd94Jz8QPswrrdnuWp9mcAAJuePhjYFgBik4MFX6WbhcqmZt+cIn68kU8C/12c8zc45z/hnP+Yc76VEHLXcTi3E44b/0NCu2m9lU/Oj3ZYxKjZoNku6G1elefQZz9n7guhOWM7tp9tz+Mu0jRdDzcMpTQ4+IowpRNrB4AYnDCl7FbGzGPkVsa8SeeMeT8TEGSzacQSSY9qQGgxGk//JKTEYgBA655d9rKMMWivSwiFog2isnb0jbLHEtOqRybabwXEc1StTs2IMJtR731fiC+XKqYMT0r7+noQq+kbdp284PsudaqatxB4hByvrC6WT67PbapMiatd0hjlcr37jpftaffvJy3KFYsQYVRo3deH335xFbrWbUFv2QwwdTficRWzyjpQXOtElQZ7u8GZUOK1kJ6TpW+/HIk5czDl8ccw/eU1ILEYEgc7Ac6xv73tuF3PWCAfff1U9wczf2zxsTmdkwu9RQRf/4CE+88imL7rHs8yI5VC7wMPeEhI6u8iT8WqoLRKby2oBw4ACFHGTFLU1+c4qrtDgufqs0PPjzOvitTa2gpCRLiQMQ3fnt4AmQBqWigZFUaJRxkbJEIx6abhLuVu4nbllVeGkDFAzQwhlkxCy3q/KIXlE8BU0Rdw3SOiLdSWyrV4vOXXWNX2IACgV22HZBgoq5wQevzjheuXNdrT99545ok7kTcJv+JkQScUXCLQ5nkbkvtzxq4uXYUFw4QA58x9DvUVe978ifqwrm/IU0QwkumrpXQVDtO6qsj1TvMxUsY8cIUmB/5JlNUIEY4XHrztVaT7Vdz3f904XH82AB2SAVymfQ9XffGreOeXvm6va5GxbS8FE/KVceMw+cEHEJ8yBXJ5ObiqQnlhA1Zu5lgaX2d7Kr4VkJOMEUK+RAjpAXAqIaTb/NcDoBPA48ftDE8wukoJ7j9HQsHgTkjx06AUCbPV1q9/HUe+egsyrztuwYqZWF/54Q8DCI9nA5YwIKNfFT4oFkFyE7B4bGRvJGIqY4MDIlxzxx13YN++ZnNfGj42vhotK+Zjx44vmfO8j7uJdgAA0iS8UtRdWDBp0qTA9gQEO19+Eb2tR7B9tTdZUjRFF4PUQJdIih/SU9BYFofTe7Gxbic0loXEdcRiY2vMOVpQSjClSoR8q4reuoXCMTmcjGk5RF1/zlhRxzhslMItOPbt24yKisOIY7iuEvnCe1x3n0kA0EcQmqywcrGPjGUuagCPi3d0ouzki6gj7fAooE9xVLmNfc53NVLJIkQYHjzgRSl+OI1P9mE3G4fK8RMx5XRH79EzGwEA+zd34O93bglsH4ZztjC0SRJ+t3o/1ux9axRlDaeM3QagGsCPzP+rAVRxzis45184Hid3MiErMSgFKyEpIkbd/7ionDL6+5HZtQssnQYbEnFvWiwab8dnzgzsR21uxqR5lQCR7PBgWDWlFNr30bcv1QozOtu//vobALw5YxbICHlowyEWi0HXHaLS3DzXU01ZVCHMRcdNE3FdQglghkwNs9olO+CoFT0HRW7AC4uPrRlqvvjJexfgkrl1aKw8/r0xxwr+xHgLuwpqA8auAJCGE7bMLq5CAQ//8QAA23d8A1nEoEC8V/Lufshbx8jHx6dcnV82PDm/xfRJK4wF353sOXX47sVb0VDUio8uFWGKYWphjhrcpYxt2eOYS/6z5B9GiDAW4Jzj8O4eD4EaavJWSzNDfH+a4uNx08oZ9vxP/uaPYrkm/AwP7erF3o0daG/KXUBU+fGPAwAGkkCfRPHY43/Frb/5o+0TeDIj5+jMBXSTeBUBOA3AGYSQZYSQZcftDE8gZmYdxUjNkU9z8IYbsf+KK7Fzwenouut3AACaFINJbPx40CJvPlLTdR+CrEiom1Juu9fTEGXMHxIMw65dTTm3Y6GtJcTjLphfDVqkIDmCXVwFE7/+ZUlGkikACLJZMYAfapkNd0lZT6tQB+pNPzFDYwC8g3tm0CFjHS2CNMYKTw4lat74Uvzy2oWQh+kWcLJjUzp3KyniE2z6NB1txOlZyctjmNbvfV7vHhCEmZXFYHDgI+RP+DH5IgBA3peCfGgor1+po8WUYcKPADBoVnsmY86z0huLMLMwgS9NqUYt+xUA4Nypwgw2cywIkiuBf932Dnu6P33y/9GPEOF4oWlLFx76wQbc/98bsG9jB3TVwBOf+yOY0QM9/bL590N8Px9WzsNHz3YS8pPFJSiurMb42d6GPw/cuiHn8Wo++xkAwOLdwK/LSvFQ/Bt4JH4Lers6cm5zsiCfBP6PAFgD4FkA3zP//+4xPq+TAh9smY7b28RDzEoj/0E3OoQcSlyhnmnPPI3Kj38cVTf9BwBAbxUlvLKiYEgXg4Xl/aXrcVAqlKWsOrITPTUrxgoKnKRqK5TIWUjo0aWMsQENZ2riV0hYNScAJKDgY5mVuH7wXLR+fwPKysrwxtbzUVb6Aeh6zKZicnIF1v5V5IfJMXHtHQdT8Iej+juDbaTY+PIRrzNCfjig5+/y328wJJ5y5WAQgpju/XOQHtwDLhPQXhVPJIIqLwBcv3X/qM9zpDSO3lR+oVB3jpw+owQvLJmF/5jgNLvvaRN5npljEKZEDhWy9y1sjRIhwljj4PadyPb+BK17t+CJO7fgiTu2oK1mEdT+30HPvAymN9leYv1yKUqT3h+Eqa4OtGx7FUz35osN9GSx6s+7YYR8t5PzRV9mwpzStMGekz+ZPx8Z4LMAFgE4wDlfDmAhgLeWm9pR4qJb/oqW2v/Cq/sO5VTGwtCv9qMrLaRXqbQUNZ/9DKo+8QnPOnJMwSsdfwPgDlMSVJT/Fru3rkR728i+ZmXl4jFILqKoaUIdUdVgnNwau6yE5pjpdZaPtsE1hgsuuACDgxUoLb0OImPM3CFx1K3soPnF6szA7w1saMGBasnct+dx9Aj54Et1LiV3QQV4LPj15jGK8sIYXt3vNTL9A78KWTXjqbCknNnmpod4uBnvPzrHoC+jL0z53Av5/XlpbXsYAKDXF9gvt1upi0GEM46FM36YiTEgWidFiBBBoOewKPjRh57G/2fvu+PsqOr2nzPl1u0lm2x20za9kQIJLYFAAAEldERFEUFfBBHRlx+oKKIo8Poi6qsoiggIL6AgL00InVACCeltUzdtN9vb7TNzzu+PM33m7t6NKZvkPp/PJndmzrR7Z855zrc8XwDYtcHZ7yix50xNzF9fdVLW41DV6dp89PYPsPqt3di5zlt/MnLC8QCAghSwQ5bw4hFSGikXMpZiuggIISTAGFsPYOLBvazBgZAs4ktf+hrWfWU9VCm3TlaurcVnnv0MTn/mdMd6QgiKFy2CVM1lKsSABIV6LQCqqqGzfQTgE0fmbeuN8THImKJ4JQiIocSvzyYMixhz18PJAsOCRz3FCq3l2kllvuuzobi8qt82eeSGSlv9SxYUoUwo9rShJQF0xjO4+dFPzXWGQGp950owm0acYCNmyzJZskyVgRMdd21Jaa8zWUXpw5LliD2Jb8I/P/8cfnzRFHxv1FDj6OZ2mahgAJQD6EqdVFOM1MJqUNn//Yyn82QsjzwMZJI8XphRa9LmDm1QE7zU2IwxQ5AVWeRuEj1eD1BgJBcdl1VgUU01vj+kAve+8h6e/TSLyv8gQS5krIkQUgLgRQCvEUKeBTD4bX4HCLIoYPrIKjAht05W2b0bvRk+I9/UscmxTSgsBI1xNXNZ9o+LUTKKb8Cxn9ZYMukVltUoP66mebMxRcL/Kbmgjl9Plp+fBLO4u/SXyCBjpmWMWorpcsh2XznUBCyrGNpvmzxyQ8TmHj+lKg061EcE1ufZogYpp86kEbsorLjLKoYd+MhyNwc/GHhX0F+6Oe1DikK17UsIQ0fHO7iudgi+N5o/R/YyYET/J30AY8ZWl4v8RQr4vyM9OdTNzCOPYwWJHssbkuq8H1p6IwD/7H05ZPVXbY9twJ4fvG8uM/i/w/Eur0GDBLlBQra9ig8EfoP3nv3dQC79kCMXBf4LGGNdjLE7APwMwBMALjjoVzaIIIkCZm7JbXa98ebzzM8vbHvBsU0oiILGYmCMQXRlgn0pNQ8AoCqKrwirqI+i1ZoVY7V9mzeOh2p6BqMW926LV6D00vGQSnmCgV8WJwCIxf5B9Qb50nQtqqaEocRuXa/giKXpm4wRcSgKSr2EMo/9Q0SyCEJEDvkbV320yBgELP3oUoBRnGibQBDGIAZ1a2rIpotn62BJeuCWsYyLjGllzsQDN1lry6gYv2QNpn2wDpptm+RT/slOxgCAMGDd2la8U++NV9wv6D3mGWWFSJ05DLTA+R4/+M6/V50gjzyOBjDG8K8/rEXnPqcKvppZA0b9y52JkgSmv9+pDe2u8AX/8Xf3Rp+6sQHen0QVa58MIfh14PcDuYVDjgGljjHG3gTwBngc2TEFv3EtcqLXdfPmuJRtH+deYkEBQClodzfkoJPwBPXMQyXjT8YMK9YIWoHbr+FK/pR6rWuaJur/c8uYMTg1N02HkCkEEQk0VdGP6U/GorOrIJZ55QUMb6bppvRx/9jJGBH7MDsDkCOnIRwt6rNNHrlD1l2MTCIISyFf4pXN+60oYTBKcXrXTkfbb0/kQfDiTn9h4P1Bf7pfbi/4det3oEelaM2oSNisXLLgjUF0kzEDz6/yCkbmgu2trvvWv1OVMUASPN/x+j3dB0XXLI88jiS07Y5h+6pWaBmnd4ipe5Hp+YvvPmpLAnu//z6SmyyCteh7P9R39E+Mad7Ro2fuWyABPpZWEMvStjUgg6F/q/zhRF+ir8MJIb8jhDxPCLmaEBImhNwLYCuAw1u/5jCipNMq7SOVOTMBh/3iF3hvz3vmcoHslLWIf8yrzu/62rUoLOOxUu83P4f1XR+CgEBgBEpG8bUnGcSJggGq4S70c5UI0DTRJGM7GrhpVpC6EWFBEFHA0mefQkPvOl83ZcGpw1EwvwbDbj0BhQucyviGIcITM2aLM7KPTXL0bASLr0Qwko1wEYhSdm2rPAYK/XcgBGEpi8yFD0EbK/KMYQaKYmqllgfkqUhuncmPnDxwrj43WSE+HWSTTVamMaUASRWBj1rwTrM10y4KcqJkj0FhWVzjmxIp3/X9YWe7v/iyQXyFXj5IMJvgbkO71yqdRx7HElSFgjEGRvsXLweAs79xEzK7eXhP+1/Xm+vHnnAigtEoGOUx0HUzKwEA1/1qvtnm+V+tcBxL0N2UzGasuLmqEj8vrURb/ECIVh8c9GUZewy8MPifAMwCl7cYDWAmY+yGQ3BtgwpPXCrjlA9vx3FrLVOnUGwFSI9fvgwlF11oLoelMDpSLhOqPmik1q+HFBAgBCZhb2ILdsY2AAAkiFndlGbwPJgZgA8QhMOXYNWqcxxtNU02yVhn51IAQCCQhAQRRCLo7WiHBs3XMlby2TFWHU7X5uRK7upZvXo1P49+nWJwptnGHu9DiAxBHAYhK+E6cjW9BiOiIW7NpMUyIpK/q9kvHvFkqQEAIBV8HrJmkaByKiCYchH+AxAMn3ZlNwpd3hiSFT1WJ84AhN5rhtCj4Gf/WAeA64qVhLr1S1KhKF1IJBpsljGXxp0n6SQ3iFmyJkMuaQtqc+2n9yOpIY88jiYkexNId/0KYNnJ2JBaq/+fuuAsEMkn+1ujSMfjoAp3/5/z9an45u8XIBCWcNqVXJqpc18CiZ4MUjE+MdJ0cfHpq52Z3k+VhNHVcYDCFQ4C+hoNKxhjP2SMvcwYuwlANYAvM8b29rHPUYvOAhHBTA9Em7J9ZPbx5meDjRtIqkk8Vf+UY12lLkgHAERJwWA7xmxegoB4IpGFjBmWMWojY4CSOR+9PU53oKZJtgB+oyg35W5TUUCsox0NvWvNY9ZpQxGaXI7yq6c4juNO39e6+aC5fTvXFFMF49jWwOcOvmYMKCjzD9IP+WSD5rH/KCsIIj23AspxZQhlI8A+3GIkLcdF6TlgRIaoWTPHsDwJU9LOepY5JMj2i/5KBjHi1CJrziighfx+Otp5vAkTCYaBux4ZU/Hektn4aOmZJhlLJFxF0bPU7ewP2chYoatslDKlxPycsslbdCcV/OylDUj6FDnOI4+jFY2rVvW5/Zxhm/Ej6TpzmRDiEFI2wGwTG0ZjIISY49KU+TzeeNjYEjxy6/t4+HtLAAAhvfKNnwDCQ68sHdiNHEL0aZoghBQSQooIIUUA9gGQbcvHFOpDFgl7fzLBqL//HVJlpbnOXoeyKOD/9QTr6szPbT+906pJqY9wCZLB+voNvvuKumCrRhiYbTB7++23zc9DhnBSpmkyVD2AP5FoAAAUFHRwZTCJYOealVCZAgKCL6Xm4TRlEiq+PBnhia6B1zX7dytg+NlISoZ4xWrF0LkQZOvepfA8BEtuxNSNj/reax77B0IIWEkQkASEXJUEMseXG408+52jzEA5KwSDAEYIhqlEbyqgUrW52hnrX7E1Byj9HEOrjTrkL9KUgemB8kbtydOGf4iQXifTXvrLyLpyu/CFLKSqPwR8ZusAEHVXaghbLhG74v9jHzbgz+/vwN+W7kQeeRwrSLR7pZXsuItcDQYBF9zyfVx0Gy8KznyyqO1kTA5sdWwzJlgNayxNzVRcMWtEn7ma4evTv+7YJ7BnKe57dRNm3/Yk7nupb8J4qNEXGSsHsN72VwZgg/553cG/tMEFu7j5bxaJCE+bCiJ5Y7bCUhiLxi7CtdOuhUQkaNSWam8jbIKmwDBTUJ84l9nKGHw1tQBXp07n7W2WMZrwT5+fPn06b2OzjEUiPAZo29YTIAAg+iBiEMEQAlklLtwDN/H4uLwvT6hAxnUPzHes62qmCBQsghw9D4HCL0EKnQBCApDU3OIJ8sgNsmBZZzfGnDFS1MhY7IOTyJlejNr5Gq6MBXFzF3d52n/h4OuNkDd2+e88AKj9ETrm82QZ16132AnZKtTNmM3NmSVmLItgfr8QsljUwi4ydkaZdT3xtPV+NugxZ/tLBvPI40hEvJO7CCt6E5DksQAAUmC9m58Ep+PJa+di3NyTMWamXhTcJ/GF2SzKQ0cl8cEzf+uzBNvqt3Y7xtkbZ9xofiaM4Wfyw/j43Vfwaeh6nPDxTft3cwcJfdWmrGGMjWCM1fr8HXMB/JfHnMVJKaOOskcADyROa2mExBCqIlVQmYrt3dvRkepAZ6rT0V6gGVDKVYGZj++HgECEAAl8H3vMWO+7e1Bps8qZ16THxWjUImMV5acDAFpaRnMCps/0BeIlkq8++AC2r1iGnlbuV/e4KdtzC4IOhCTc8IczUFbtLLotBiZCkCyX6vDf/CSn4+WRGwKyFcM4NOhyUxqkwmXpubKMRx00JrZh9qrfIJxqhwgCWWc/yzreR1GQW54IA8Qm/7T0gUDrl4wx/G5XC+rjKWw1Au+NXfTkFWLTHXJYxhgnQp0d1Y5D7i8ZonrH777iUllCiW0yViSJUMZxi3hvyiJjmv5OvrB6/7I588jjSESym5Ox+q9MQG+Y9zlFIQ1zynfjS6NX4IyJVTh5bIVjH+ZHxhQKSebxmFuXfYSlzz4FVbEmXzUTnUl0y19uMOUxACD21lt45tlazC2aBEYIYgLBs0E+7iwQVx+AOz1wyEdQ54iydKFjWaEK4CJj9Z31oIwilulBmT5z/8LLX8BpT5+G+U/PR0+mB0IhXy9SBUwv8eCXAeaRxbBZxqSSICZM8GqMGTMGe8yYMTgxJoCAoKedi3TGFKeFQ0mlsP6dN/DPe3+CP914DaimeXz47oD/Utu4fMmts3HVz5zlLCS578dryKSpfW7PY2CwW3FuHulf2cCe9QcA42T+I+6MrYeoW3FHNbwMABixazFiagqjiw9s0KtBcG6a+8csDYB1sSQuXbUVSzpjQFI1SaBx9aJNhJkxOxnj63tccZTqfgbVq4brxMXlrhkawqZ50xA9pQqZGWUolERoNXzyEbNZxoxxYfXuf9+imEcegx1qWoGaUpBK8vd1cfeHIPpUZgjVMG9IA56TzsAvLzvOsR9NKOj6P69GH1MoIiUljnWv/f4B87PgDhcAd1Ua2HPDjcDmHVhUyZPc9kg8nOD5gii2yIMrZjlPxnJEy8jPOpYzWsZjGXt8w+MAgE2rH8VxT14FAEhpljXplP89BWPfeB0AINjUzqmvZcwJu2Usvb0bx7FRAIBiW0anRcasbEqqD06M8VqS6TRfn6YJJEZY15aKO/WUNn34HkgW305xUTFCTEbIFiBZNiyKogofxfcsqGhbA7GosP+GeeQM+8tcpVvGlInFUOts37PrJ1Uynfi07XXsim+EqOkyDYR3WJKagkgViDlUUhgIMgp/BstD/vXiiPEcMwYBQGCVMyuZAfg8+RvCYW6gb219w9y2ectPeRuXS33rZq84ZC4wrHjaaP4d0mL+vX74/kxoWhJyWRi0KsytZDrRXbmry3wXSyO8/XG1Je5D55HHUYdHb3gZD39rMdIZbr1SJIpCxuOXO1kpRqWexL3qlSiLOrO9E2tafY9HMxo+d/NtjnX1Hy2xLXmt7B2NcVR+2+mCDFIUgtMAACAASURBVEl8bLpi+DB0CQLuqCzHldVVfbo8DzXyZCxHDC0vdyy/sO0FLG9bCQAQirh7oqGnAQDw89Z2VGn+2VOdAQVDf/wjEGaf2WfPngQAHG+RHKNl8k1uVctkLJMtYwyzZ8/2sYwRfkRGINmyPo3xioQlTxHvdCKe1TKmqioEEKfKgQ9v0/ooa1Oz520Qyb8kVB77B8MwVmibLWojC6COzZ5vE6AZbO3lOj0iVbBsHIGU4TXcinoaAMYg5Vi7NFdkVE78g6J/WRSxKQkwhg5FAwVAYi7BRwKUogvJ5C4AwJatd5uburv5vbjJ2P7g2keX45nluwEAWmUQqXOGO8ogdXYuNV+RqqBsvi8vrG7EEx/zazMSESZW5SceeRz9SElFUMUw9xxBABWB0WQtAGAdqci6X89i/wQXplIUV3mz8VVFwc41/gH4rz60DsUXX+JYNyZqRVbNG1kDAEgLAlKDqHxZv2SMEHIPIeSYKAzeFwIhp4DrPZ/cg/uX/AIAINVUgzKKNa1rAAA1emr7VMG5DwAseGYBhGjUQcaoT90tu5vy6b/fiQLGA6qHUj7DFiBAEASk05YUQXV1NSKRCKgmm+WQGNNA9PgwAkCw19TTpSmCI4ugqc6HsqCkDMTlZjSuKZ6IAyAOCQ53fBmQvcbgGe/cgLKuzb7b8th/GL+POAAZh4A+aRACk/D2dIY/nCdgW/lKnLT0DpR11UNCFAHpwAolMnASLiJ7Rxha3Ahxey8Wt3WDeDSG+78/1lemQo54Y2OzLdbLOt7j7DIAQEvLK2hMc6LY7urU1+7h2WSGm1PZT52zPPI4UmA3KmhEBYiIazOyqXq/hdTih+dPwrPXn+TZNzSp3LMOAFiGQgp4NRPfffxh/OPuHyLZwydLC66aiLOv5dJMqbgCuWoIxEqL/GUuuw7D2r3jUW/3/lnMDwZysYw1AHiUEPIBIeRaQsgxOcULhbzWhb0VQKYojNtnbsFxjx3n2X5rcKTvsYgsg1C7Zaz/mLEaWo5L0nMxjlqzBEmUzKD9y9InYVR4GARBgKZJoDQNSlXdMmYkARCse/d166CCUSCamSWSzPMLgoeM2ZEgaThqUhICGo9D67JiY5hPoPacZdyKsfW4vNvmYCEbV/kfdq1nnaj/RsVJhj+eJ6I3QpCWgbAuWFyEaZDFA6uRZbj+BDfLckHa1ou39/mkyOuPZVPjuKz7Epc17wAYygAA3xlZZRZQ16jl5p9X6uwWm3tTSGY0M5j/uRV7Meq2lw/MReSRxyBEcq8ttpQmwQSGm/bsRDS8CEEhggXHT8S188Zg9sgyz75G8H5wTLFzvaKZAfx2rHrtJQBArINP6kNRGeOOt+Jk2xtjEILOkn6/fsjbj+1qbMrx7g4+cikU/gfG2FwA1wGYCGAtIeQxQsi8g351gwiRoJeDJkIEX7pBwcYRVk9fbhN8nMkkvHXZWxhfOh4vXfQSxpaMRVAMQh4xAuGUpY1iWJgMLTHAX4GglBU4SJpsc/MVshBaf78aytYeaBpfn0zuclnGCFa9+Yp1QD3GRUmmEOtsd5yLMQoiW1a0iq9N9QTwG9ctB0WIsoCtZ5yJzSfyWU9ixQqUfPwsAGDEFD7rqdnyfRTEuaUhLA6u4MmjAW6x4G+LWxzLpeiErGce0qgEtTYKUQ9sTxfuwfVt3AKWsf00hIjoEv1nrQAMnj8gGBxdIv2QPJFA3Ocjf6IXAO6NZb8uAoY9eyZZ56z01lodGPg56yKWm5/a4kHt6wGgK6Fg+k9ew8trB09nn0ceBwtUo9j6QQM0ZTc0pQGMJaCEVCToPEwsOBVji2ZhwUR/8W8AYGkNcnUUlV+fjtAEK0MysaoVRMhOU8IF3PskB50d0duPb4KyZ0+/183W/K3fNocKOcWMEUIE8FJIo8BLJNUD+D4hZPDcyUFGOFyEl08g+NkVfX9lv2y1SBY2vojKSCWeveBZjCwaiQW1C5DW0pAmjodc4Z0dnJeZZX52W8b8ELAp3xvt1YZeaHpNrqUfn4VkogGUps021OYeJQrfp2vbHvzzHqfMBGMM21Z8bC5LFWHPNTHGMGL6lQjr6uhaN7ditP3hj+h6+hmMbngZly/owsILyjF7xS8xfi/f3l4ICFd/od/7y2P/YJDmTcxbn1IR+G9FK0JQJ5dA0F0LkhzFN7/LZ5lpW8bl6J2vYM727OciA+TUGmVIZ/SKE6SfeA0C/2LnOqiWPeYwkShBU6Mt41hlaOnZv/qUAEwjsGS7Ho1a6cRhUUBlwLqesmgAio+bvr/qA3nkcSRi8cPrseTtOJTY36HEngOjCWiRDBjjVq2IVICCUPbOIrWpA0ojD60pvWQcKr7GM+3Tmzsdwq9ujJhSjJMuqkPNBKfEhdCPsGCBxMXJa8+5qv+bO0TIJWbsPgCbAVwM4H7G2EzG2N2MsXMBnHCwL3CwIBoqxKMLRawZ0/dXNiuVxiPqOVgpzeArbH709e28AOqsv81CwcmnePaNwDLH+tWNdCPUa7ekEXM/zTZItbW/BegxaXKVM9sx2MTbFQW8FgZGGVa9ZrlVhIgM0fO4MChKBUJR50vW+sADIMEgCBhEJQlBy6C4Z4e5/Z/XjMCCs77R7/3lMTDIOlGYVsh/ZwqrYPVP2a2++zCqq+3bNLPStp+zrLMedS37fPcV5IETizv+bx1WrtOFUKHhhAorCPcPC28Z0LHcKvt2pNNRx3axI405P39zgFdrgw8Zi8WsuMewIOCZ46wqE29t8pcD2dWRFzrO4+jDthXObEjGEmChHryizQUAjCk8rk8LFwAI+qReLAoiWGeFsWjd2WNWGc1g1jkjPXGkcsDbN1B9svTgwgfx45O58eGN9rV9XtOhRH/lkAiAXgAzGGNfY4x96GrijcQ7SlEYKe63zZxABQQA84U1eCmpa2j1NgGxFmDnR5gUtsy0QlEhRGaRr+d2PgDVVqTZq3bvheTz8wkQoGn+M5DuZvegmj1LjlENMdWSHhCCosONyvdm6NibRMvOXvfuYHpMnNbRDmZLDlg2juDnX31uv2sF5pEdJbKE/5s5Fn+aMgoAEBAs8h2E1yo0gW0ApRKkyDkI6fp3JyeSZrWJ12YS7CkHurMkW1BFGHDd8Kc+2WV+FgnFlWNeMpdlwWkpIxnaZ8WA/jImKT3wyeISIRhadSEAQFEs174sEJTL/WcH2wVh88jjaIGaXgMlvthcJmCYkRLxLptmrhNtYTWpbV1of2IjGGVIb9fjjDX/hDCtJzsZSyf8JzelQ6Ooe30xqm63ZDEERcMjZ/8Fpw4/FdMqp2HmkJmYM2xO7jd5kNFnb8V4esSFjLFYlu2DJxXhICMSscygET1ofnrFdHPdXSffhf/ewmf579AZ6IFeo/H+ScAvxwGPfAZff/PXZvuN6V0QmMXeFZoGZVZHnSaudH4fGJaqUmop3QsgWd03atr5UKvR7DE7L//mvxBXu/GPhvtRcw8PDyxZ6ExIYGBZ3UhE4PfW9vsHwVIWESiePQvBUNR3nzz+fcwtKUCBbuX6fMSq0lCFZk/bH+EOQBMhBadA1GeNv25pwyRdLoUKwE+vFLPqjEXL0wMvHG57Xng+7v6Tcsb8u6+PPrwcQN+Ws/5AXcknRm3MoEBMIWU3olnqWNqRd1PmcbQhFVegJt6AlnFWSSSiYPp6lKCC2skWMWv701ok17YhtbEDTK+qUbjAWdin6js8bEfr9ZfAAaxAfgOLvjMTAC+LFKitRdlXvoK6V/+FgtNPBxjDrFJ+DcMLhuOxcx/D+NLxA77fg4Vcpo6fEEJm9d/s6EY4bBXALtTJ2BQbuVkglaFEX3+3+kV8RCd7j2EzI7zW/j5UyU1KrO29JOXa4jVBGKWS7LFcAkjOg1BsJI950bIMLnybRQpDFVZGaZ02VHfBCpi+oMazH9OsY3bushV4PXV2TteWx7+PrkarBI/kkpEYBqP6AycZgsS7zRBjKLdp5HUWErRW+esDCaLWl3HVF5o9AxcMgUA/5ZX6KJ2UjcipKo+VY2z/yZjmMvl9d3w1bhgxBPPLCkGZd6KUybSDpPf2f9wDUGg9jzwGE7pb/N/hjBDANXP4BD5cVAS1PeXJsE9vswSSAyOtJLmenh60pXV5mA5rnK0aw+tcfuPBR622rVZIgDt2DAACo0YhegoPC6LJJJiiYOdXv4qeV17xtD2cyIWMnQpOyOoJISsIISsJISsO9oUNNgTkAO5qbcc/9zSZw8n4HZbXNvTYIgDAYm02KATsYUM8xyAAAvrD2FkAyNGzHNvtEhcBOK1bqaFeU62kq6zbhySBCchk/JXwiWuAYcSo85ebO0eWRQT1wXuuMlYniAKKh0Q8bXvfsOJzur/3AwDA978sYs7cK3I6Vx7/PsaP9ZF+0B+BQnDXMqOchElhTtYaaBVk/TkRGDApnYHE/OMqxH6kKfzhJFCRSE/fzW2nCLhKOYERxGLeztfc7OPGzLUsEXW9K9MKIrijrhoiIWDUS8aWvD8HHy1dAPGMas82O/JkLI+jDS0NW33Xv1r8RVRs4u+b2pZE839/it63dzv0yGIfNgJ6gD6xWZbvv/9+/PEvD4GERFCbZeyKO+/B9X96AgVlVpzz47d923HeYMTrGRLCPJu658UXoba2IvHRUuy95bsDvdWDilxG4QsBTABwHoDLAFyq/39MQZJEXBSLY6yi4IHmNlzV3YMRimVtCOoP2L3q51FREMSQwiBama1UUbgc3bVn4pOdu1EAAe1FBII0zHEOYtMJEFwDCdWJmlxjCcmKpvHMaRlLpbJIwTH3Ij+mQHKMrSEEwygf/IKQdTelgFTMa0am3V59qIsjszGssO/BKo8Dh6EV/vUpAetRYDSIYKoDwUJuDbs0cyfawvz5iYoanmnch6GavzyDW8srJ7j4UbzLme5eHHA+N+IuK0Li5pN+7djGGMHKFc4yZQbq6uq8JwOw6Hcf5HSZbo1We3yw3TI2X/gEY22yFtFo3+mleTKWx9GGeKc1wUkVWB6dH6XGQevRxwb9sU9v74LW5TQsUJ2MdcS7cOedd2L7dit9m8iCo4C4HAwhUsTH1flfuoafM9aLje+/gy3LPgIAjJ87FIGwk5ARXXOs+ee/gNrulHEaLMhlFE5m+TvmcEXZ33HVsBcwLZPBrR1dkGz9qtFXb2fDkFI0XDtvNE5N/xpbTn8Q665Yigmd9+O5HdyxeM++fUj59NlFkkXeBNdPY6j0R44bYsZwGQH8DsuYvlRacqHPHTgHAjpQH5NAcLoyBded9UU9Xo1bxoxgS3nEiD53lwq91sI8Dh7CwezaWoaLj9EAZCUOMcCtqRPH1uGD2tH40zkCXjtRxMmp3yB5+rmoGOYNG5WJMmA3pRutO+Y6lm+a9ZBjWUhaLtOh4VbQQhnKWP/Jxozj/oKJE14AAFMMeX/hVsy3F2Gn1Jp8fEO7F+/PtfTMWjIqWB9p9W73Zx55HMnQNIpPXraScipDvJ/olrJYrBk8UhUsw9/xPS3czb9qlZVhTWQxq7TFjHPOBwDMPPdzeOW3v8QLv+SC4tHiADJJFUrGVuUmaQX67735Oznd26FGLmTsTQBv6P9/AGAXgLcP5kUNVjx909mYOWYYVtMxAADJNRJ9TCeCQcD1p9ehJBJAGgGc9WoxPvvodmQg4z6Vu+hOTabMjLVA4ZcgR88FAMiQsCh9AiarNZiiOeOwDMuYfcpuZDfar8IgcUTwDliMOQP2P3r2yQHcPQDC49RK9MxSbm4mEHXzMo3HIY/MTsjkIXkydighSV6dMasEkU7GNAET65+AKPO2f/ry8agtK8PrswRosojFP/kiPn/ZT0AEv/qp+8HF3J5GzamuXRzI7raUoSBz8hBodf61NpubKyHqArWaHvdGcq9d78CHW52zZ3v0GXPFjFGX2zK9MLv1150YkEceRzI2fdgE6H1KbySDq8o244yfPYRv/eR+3/bpnT1gdv09iaDrRW4JE/Rs5DVr1ljbRYusuSEHgjxD03a4VDwGOciPo9r2ixxvqXApe/uP7TwcyEWBfxJjbLL+/2gAJwN46+Bf2uDEl08aiQLdMCjaZrk/V67ENzPfxkvfOhU3LBiLk8Z4tbuS4JYKEcBVce6OEaQhIKLVeVeyIpysTjCD8w0YYq29NlHZfYIuoipY0hIBPaZLUbxSBtRFxvxqYvYFQ45C67AfW8Q0PYCfxmKQSr1itgBw61dFhEsqfbflcXAg+Oj6TAGP/zKeXEEDimK7IerSFuGAiJIo/xxiDAVBCQXhUBbSxQbOxlzZtwYZC+o+95CUXZhVhtsd7jzWM888Y8ajGJax/5p9JyL78dgxlwXLaRlzki+u5Zcb8m7KPI4mtOzqhZbh0jfrxrRiMeaiZmg5igLeiSAALl+hux3FkiCgWsvhqHfmlGlNILm+HV//6Z9x/UNejXlNVbHy1RfN5VQsZgq+2msjy1U+hgBCwLQDW+rt38GAhXgYY58AGDziHIcYFQVBlIjc5224KcOU4p/aqWhHMSYM5QNZbZk3qP0Lc0fgrPR9AIDhQatDJ33EbO1LNgAA9m7eAABY8/prSPRwEpYk3qD+EIyg/tHmuvXrFgAAVNeM3q8mph+6W/bxQuL6Zfa8vpOfSyoAIQRyQARTFLB0GkKxv9WivQgYXtG3GzOPAwtBEHAH+yF+xr4Haoi76uzJcFMarupInZXiTSQ+aQjaeYNPfNgBUYrTZPxgzn/j7lPuRmvrCATF7Gns7oxQI0C/puYW7NrJU9YNEjZpEncdlkY6IAgDV94Puuqy2j2PjGa/xv7gTgzII48jGa0Nq0AzfGzaV8rwhjYLpRG5T9X8lt9xN6Q7dkzzGY9Uw2DQpCJS3H8942fuut0kY5ot1kyIRlF86SXOxowhuXJlv8c8VMhFgf8m29/NegmkY0ZfzA9hXUDzj/QcAECtoiKFIEaVRyCL1lc6pZoTkweumIHVPzobd35uCrawGoxKPQFZsctaeH+GrT0r8EH3a3h339MALKuWQASk49wv77aeAYCsp/NnMlPNdYbURYo6Q/1ojmTsz9+6Fo/+540eq4ZdUoPGudq7EPGS0J9fLqA3QjBj0hk5nS+PAwNZljERGzEaO/DB+18EYJExAEgmC0Eo8NFEgpqKMeZ6KnFCH7RZcURXsfC5Q5dDkvZDwNTtpqQyxpTsRGmoG5s2zodAGEgki3adazkc5skswcD52LmTV7wwyFhlqSXH4U40+HRn/92XWw7Mfm63tIXb/e9G6qxqpE8e4nvcPPI4khHbs838fFN3F/bUnAdJFEzXYtFZI1G0MLdJuF+cp6YnmbEsMaA1k6c6lnvbWgFdqom6ypGpTU7R89C0aaDJwRP+notlrNL2VwzgdQCLDuZFDXY0CzxLrSXNB7DvdHZh0oiheOjLxzvavXzTPDTccz4unDkcxREZAUnAfZdOB0Dw7fR3ANUoZOr9GXqVLrSkdpvLBnESiQhV4YNBJXVaoQoX1ELWJTHWrrXkCAwlcrfrxXBTdmX8S7fY0dm4xzMa2smYFtPJWNQimb87n593Yy3B1fHh/Z4jjwMLZ5UDYvuXW8Y+Xf45EEpR3UNRW23JYIyMcm2gU+JWRpLboHNZ7WJ+rAEaeoxLYrKAdWvPAHFUi7CuDgBE2SI59877MQDgP4e04j/ZzwAA8TjvSP/1r3+Z7Xp7ucu+428bbUd1XuTrG/p/3t3uRLEPN+WGDf+Z9Tifu2wSIBCMDHN3bD6AP4+jCTRpZT+XSCl8djoPuTEsY+Gp5UAWMWQSsNZLQ8JmnKcdqi6fYwjDuuEXiqGp3FjiJmNyrTMOe/Tfn0HBvHm+xz0cyCVm7A7jD8BdAP7BGDumC6zdErgD12VuQVorwdodu3BqMoX7r5yN8VVZJCVsWDSjGlfOqcVT37oapfv+wlcSr4WLgTqEUw3iRCBAzaQhFMiYoY5y7qMxU59s+HCL/BiWMUM4VpCtgTdyeQ3eaXoqh7u2Shz5gequ09B4Xpy5e9JwvDtdwOW3S0gHCEJybU7nyOPg4uzK1wEAnxm6GIwJENQMRjY6WfaIUDlW79iFSQmL7A+Bk8CsW3uW5fIcCMFIWzPcZLIISXita6WMl+GSRL5NCDFUhPm6C8NrMQMr9fPq7ghbJ/7MM8/wbTYC5i4SkUOlMY870d5RegP4vW5QrSKI+eMqUFjISdj0oojeNk/G8jh6ENesN+OUVApfPXkUAIBldO0w2RrbQpOdcdTDfmBlUg+5caY/GRtgXDMAUM2fjJV/7WsI6uELZV/58oCPe7CRi5vyMUJIESEkAmA9gB2EkIFV9D3KsCtThNfp8VBtbsJIoP+6dAAQlET84uLpGDukADO3NmP0jhdR1eL1WzPGQG3kx3JTitAyCorPGeV1U+odfZDJjhkD1V2XQdOPb9Mlqw4hTd2mWn/lcuoiYylYPvz0Nm6u/qSgBf9z9/FY8f1zHW1HjMwr7w8GTIluwsNn34QTi5cDIAimvCKoYiACAcByxSp/Fe3xCp0SPYA/V89bR9weI8LAGEEHiTva7NtXB8HQ1NPJmEqsd6uh4XfmZ0q5Tl+7j24QBcOptfyZi7U5g4k/6Y6hK9F33JebjO1r+jvi8a36ebPv+/w4PilRZlfgygsm4NMefn/G0fIB/HkcLWhY0wbKrPf3JeU0CLrMEVN040FAMMclscjKnC69fDyEoPVeCwHRl4xpYn+9i3dmVf8hD+inrpiAQG0txvzzOUzatBFVt9/ez3EPPXJxU05jjPWAi78uBlAD4OqDeVGDHfEMHyRuOtvSF4r4VInPBaN3voqx254HALzd9L/mem4Zszp9w00pEBFqJo3IjEpTU8zcR3/4CJz+d0ZFVNIiSOZAYA2smua1TAiSf2q+ppMxsYQPbrvSVuxN04+4G+kv6x/Be7FVaNi22LFv3ZAZvsfM49Bh3VpvzJ6geklWS9ksXJP5Hh6gl5vrarqO87Qznr5cXW+NSet5JoyTsZGaM9Vx65a5oPqRQ0LaeSIbOjqqsWDBmQD8LXNBJqMqqstcKM53c+XKZsy46/U+r9VOmlhIxL6mp7D043OQTO7yWMbsmFhoiTJ/dV0DVvfqJcf0e8i7KfM4WtC8uRUGhdhWHcNKNtbc5rCM6e+SELLIV6DW6UVKp9OOcAMDBRfyUKC+EgIA4DRdABYAdq/j4q9uy9hgRy5kLEAIkcDjxJ5njGUw8PLARxW+s5BnnpUV8vioLhZFMIciwdkg6iQnoVoSFQzMMQMXdesAZSqPGZMEs1C4Cf2hz0BFLGaJdFIqguhlmQFACp1qbuttb4MbcvSzGD7RmzCbjBkldBiSagz2UbLkoosAAJt0b+SqjEXUnt3ThHFTLZ2XPA4dtm07HpvrTwLgXzib+Lie542rRN0pl+CjH3zGXOe2wl6ePglEz8nM1diTVp3dBgPBWM1J/BkToenXKQn6RMGnGD2jAuimXs96A1WsGKKP+9+O8T/4Fxra4r7btjTz9+eiCycgfeoQ0yX76YovQFVT6Oryr27gVyoJAJghC5O3jOVxlKDr7fcAUBSkNITG7cY2YlnSqR7ArxGK17d8gBhSIAEBFddMxdDvHQ+5krvtq39yMobdcSI+/vhj/5MUSxAikmlpy4ZgtADX/+kJx7r3ntq8/zd3GJALg/gzuNBrKYB3CSEjAHjluI8hfOO0OjTccz4Cuu7RBjrSFSw9MBA9+4PZOK57tr87vgkd6X3Y1P0JlEwahBAIuj9+ph47xjSGgnnDQQlDfX29uS+l3IbGGMWpX/gmBMmyRjx79x2O8wRLbgYRwphz0fWmwrGB5S8+y4/Xk9GJnS2oOZFAImgNOk0shZOSSdzc0YlHtG9Clva/aHMe+4/GvZPQ3MxnrPG4T2o4pXh3qvPZlUUBPzh/MsqiAW97HUUsYlpm1RyzcuP22S0BwIhZRcKOBcN5yaJIH0XEKROhbMpeZ5KAYFhh3wJjGY3imr8u8932P29zl+RT7V2AKIDq15lONwFQoCj+Okru4H4DK3o56cuTsTyOFsS7Y6DKDnQWUHx/z3/g22NOM7cxhQKSgE31m7C2eTM+lbcDAkFofCmkCktPTAiKEKMy3nrLX6tPVVVeEinj38cYoTNSIGCWSQIALb0RrbuyT9YGI3IJ4P8VY6yaMXY24wxhN4C8RgEAdchx+KN6Pr6t3Lhf+y+5lJtgV59aAiEwyaH7xVzGxzRN4PXGRxFXu7H5o/cB8Lpd16bOxGy1DgBQcFK1WZrIDkpF9JIUGBjiXdldLIClecYY8+ifZdJWzE9EKgQBweiJBdg4eQq6n38eEZfsWYcgorFtEW773g/7PGcehwaqapVHamjgbkdCVTxy1v5ZdQ1rUa6Vh3pttVwhEzDmY90FcPaId/Hw2TdBkjTjRB4wKnjc9G4IPu+CG9uzWMZMUEOXzQnVRcYKC6fwdkzBiJCXxDbroQ15nbE8jga03P8rdKYbAQCyKiNFT8SozT1I1Xcgua4Nsff2ACqFomf+EwawdHbr1sSJE33XK4oCLa4gvc1/4qWp/L0KFzjdnmqaa5ltW9GCP3/3PYca/2BFTr0wIeQcQsgthJDvA7gdwPcO7mUdGZBkGb9Qv4hOIUsdrn4w44Yf495LBXReswiB6LlgghVvEhCs2YMYmOLYb/eGNUgn4iA2YcpndtyHwPACZ0VjHZSK0KCBMYp17/IXSAqd7L0f2zpGgdbdTgOoV0+JYGpka9bR+Otd3Tjpiz9CcSS7hSWPwwNCGK5KzQeohnTfta0BACnVS1rIAOOgjFhLWhKAPCsMxggklt1iqgl8mxDj+6VSlmwKA3FIq9jxmQyPT1RauGVNmcwtgsoEf0FiN1Rb4C+LSvr5nF2lojrJmKTXlU2m9uCFWePggfFd5S1jeRwFaH/oIcSiXstz2yPr0W6TlTGQIGkI0ewdTSBgC+4vtcZTRVEAlUHrSvu64nkRawAAIABJREFUKuVAtrGFv3BvPbYR6biKRM/+CzUfKuSSTfl7AF8BcAuAMIAvARjb507HCDJ6DMzJYyv6aemPOcPm4Jr/eBD/cYJuWbMNagWyZXKVImc59kvH43junp9ALLEsHWYqv42MjR93h35YARenT9Tb6D+54Cw9ESq9BVL4RHM51plC01ZnncC2vTtddyBAimQpewHg7EQSCyf7x9bkcWhxTWqBY5kQCgEEjKrQcpiSJTUfMqY/crkGkMb0zlStK4QQAQDiaxkzmYuLaxl6eQDQ1TU0KxmroTxwP7WBZ1lqNRFkZpdDG1ng296NF1Y32i5Fzw5zJ8sw53XLOhnbvPknKJN9CKZ+nI7Mfgjl5pHHIAJjDMlQOYwXND7bWwlGLAshMqPSDN/ZI3ZAKs0+ViiKgoKCAtx444247LLLsHDhQgDA4sVWIljs432e/eZedAUIETBkjJOSED1eNJPKbl0fbMjFMnYqY+wLANp1rbG54BmVxzymDS/GLWeNxwNX7H+m4Pya+ZAFGcGI5FD2Vqj1gPuVS2qs3+AQzTPbCgQ1WhnC4TBqa69GMPAoAIIgJAcZE8ShfV7XB//Y6lnnrm3Zn+rnT5Uv9nmOPA4dBNerTgi3LVFoGK30TxA0v99ZZ2MsR2tPUo8ZYwLBLCwHYwRyQShr+7BLciUSsWJAWprr+nVTGhChglaEfBMB/NAe886i3WSMECcFlWTL6hbwEaI0do+pg99dkkcefUHZuROtFTPAaAIgwNXd3jrMWkcKxJY9GWaBPt8/RVFQVFSEiooKVFdX48QTuWEgnU4jrWf/Z3b3ouetXY79Rkw9Drc89YIjXgwAIsVOt+UTP17qkboYbMiFjBk9YooQMhRACsCog3ZFRxAEgeCmM8f1GeicK669fz5g09LV+imxAgCqK1i4pWE7QIAIC0GS9OxLashdEB6TZhK7XB5M58vjvSZiakIBgCICAdvAvD6Yl7M43AiFQqioqEDNPU6l6d6eCgggkJQMftnizah1o12PD5kkNuOyII/HGKi0RVrvDK8KrsTV+BMYIwiITn0+mYmmgXhdoxVHsnLFeZ7jERB8IXWqZ70bd4FrCj05fQy0Km8xYjf8Ys08ZAwM9fWWW9+wjGWFvruSd1PmcYSjfV8DFDkCsDSiYhplQpNvOyIQqHpMV4gF+rRObd26FY2NlkXaGL8AoJdwCpJc3YqexTvB1P7HrmFjnfYiqjI8eMM7/e53OJELGfsXIaQEwC8BrALQAODZg3lRxy7sT2sOnbbE23dlWgEAj/+/m7Dm7dcggkDTZ+AGGRNMaQvjJ8/BSuCayXgsYxBAdIXkMS+9iG/dSFCmZ7d8sbsXX7jgfORxeHHrrbfim9/8pmd9e/sIHnWlKVilTO/3OIZlrIikECWKg5jnOt9UdDJWqCyBBA2MEQRF50SGl/jiz91FY18y18di3tk3YUAE2V0fBkZhB54Wv4axygc59Xh+b0YIXpX9dMqK5QwEh/RzUD3zdJDPzvPIoz90fPUG7Bz5GTCWQkhQIWUZS5rW7zQllgTAMZ7s3r0bjz/+OBRFMZUD3KWNpk/n/VJSchodlH3Zk26mLuAhPV1NmxHqI0ZtMCKXbMo7GWNdjLG/AxgNLgI7+ORrjwLYXZNNie39tu/t5CTMnoXZua8RAgRToNVjGTNqFIpVIEI/chOuMi8qs9w3jYltAAgE/TystAgdEREX9cZxR1sHvtvRiXnj+pYWyOPgQxAE3/ptAH8mCNXQMP4/cjgS7zCH0VLUaVVIqr1m55GrsUfVRRglwehcCQRRL2KfiuKczHFYqEw3C3sLGafVrLFxfG4n8ju32oX6DTeB+Vi9elOuwt8++4+G932MRsvMz8uWWZpGqk+yg7ktz8UAcGIeT+fj5440qG1tiEf1UnssjbgQwT+Fc33bPp1+D++++y4Ava+xvXoPP/wwtm3bhvr6emzdalS2cL4cp59+OgAgJTqfk5b/WZX1+s7+xk0AgNZdDZB8wngGM3IJ4A8TQm4nhPyBMZYEUEYI8f/2BwhCyGcIIfWEkK2EkNsOxDGPZFBoeHrHvXh6x73ozDT3237vlg36J5taOChECGZpCS5RYQQhMxBdPJYQgspRzqBuN9xK/JRpyOh1vz5pfZm30S0kCX19MdVweW8MMoDSA+C+zePg4dU9D0NgDJ+dXtdvW0kn3cNoJRYoU/nEQZ/R5pohqOidrUx45zpOrYYgCVjy3lVY9snFqKUVCECCoD+vGcUZT9a8r+/rLCsrw/y52d2WAqhvtnFrrzMAWRb7txozEIdbZe+eVvNzJuNTiNzMPM2zMQC45q/LMOXHrx3uy8hjgNj17itIhivAmAKq7gbLRDAv7c3M11z28gxU3Pf0/2D7duekprm52SRhs2bNcmyLRLgwrFrpLTXIGIPW643ttOt9xjq9iQWDGblQx7+AdyVGL9cI4Of/7okJT3f4HYBzAUwGcCUhZPK/e9xjCaopFmsjY4xnyRlkjFJqBjozMIBYbp2OJk6gBGmU/wlsbS+94x4AQENsHQAgQ1MABFPWIqbxeLeoPjB3sNwy1/I4fIirPdhSTSHJ/cdRTetdhyKlB2eBm/4/bn3ZnOnSXFzqABTDMqaTsenaSAiiXxfE26UU3hkvqF3Cz+OSwXBnU950002Yf8IpfV5DbdTr1oy79I/2p5qGplkDBvMjXISrsuW9lBxLtvQfp5jH4EP6B79AZ8l4MMrdj8OjlrU6Oncoyj4/gbeD09rcIyRBKcX777/vEDRfsmQJRN06PnPmTMc+wWAQoiiCjvQm+cQ+aETT3R9DafMKQ9dMmopQoVfGJhfdwcOJXHqdcYyxn0MvaMgYS+DAJIrOAbCVMbZdL7H0FHjJpTz8QLzkRmNeMz8DhcgEvdA4BaUURuIXYxSE2B9sYwDJkixgKyfz4m/3AgBWdrwJXFmiEzsC6BaTuO7SLNTJ2fNa/4HVeRx69HRbrmMGip4IQyjUPxkrVuP4yp4nMETvMmJqFxJcnwIP7vKxBPnACF6XCe+oBRAQHzK2e9N8xOPFGCs3ozrahLNHvs2vl7oyQn26ISOzUyjwjxfxKwSh2uu4MoZnP92bw904oVGLjNFstSuJ81zHInpTClbvzl45IY/Bj67iOjDaCQAYddKZ5vrCeTUIT+UyTyni/w4QQtDa2upYZwjDGqTM3laWZd9kttRmfn613UvGymtG+J6bMmYSwZadPTlngR8q5ELGMoSP4AwACCGjARwIBbXh4Gr+Bvbo6xwghHydELKcELLc/SMebTj9K7f4rh/SshxiYILPFv4whUSLqGVo2rSEJZNJ7qZ0WMYs1yHT+OyUqvafwXt8ACDEGtw0YrwcBEzPlonpMgQxjWeVddYuzHLMPA4XIiyItWsXYunSS1CrlYMxCk3UEAj1HwQfDLpqSIIiIXBiv6Qjt7IjRvC6pHfUBMRXlbu3YwRWfHoBwkTFT0/5BYZE9OeUui1jHKWlpZBl/fnUO1hJr323fNkF0DRrv2TMmRoPON2sS7a04ZOGDk8bNxr3TnIsU00yqxpQzRvsb1zwsS76esOTK7Hodx+Yy/u6s3xXeQw6bP35nUiGyhEvGG5axmqHW0O2UBQA0a3K2cgY4HQlAjAzLs132AZJkqBqXqNDWidjSqO3MmMwGkUmETeJ17n/MQ1Vo4sAxidr+7Z34++/WI4Vi926mYcXuZCxuwC8CqCGEPIogLcBHIgAfj/rmqenYow9xBg7njF2fGXl0R0QXjrUw0UBAJM2PQEQr9+8NsoJWkSyNFUSao/pNvqv//ovaJpmc1MGHaQqOwnjEASnmO25N94KANA0/qKNnFKB1gd+DQBY3s6DKreoozEq9STi1X27i/I49JinTASlEpRMBGcoU8HAoAgUwXAOyvSut5Uxaq7K1UxuWMYMNyVhgNKUPdidMXc2r7O7Mp7rG77xTdx2Gw85NWe7ekecTBajt9d6jrv3eV0eqo0g9aT6LhcGAI17fwzFFc+mURE93UP0z0n8Y0YdCtxWP0KOaTLW2JXEe5udE+qW3jwZO1KgPPY01k++BgBAlV1gAOSg9R4IAT7pKZhfg+CJ/tnFO3bsMENoDGQy3LZjV+Fva38Hu3Y/wskYzS7zZJzTjlC0AFTTcOEt0zDplGEYPb0CY2Zw7qCpDPFuHku29p2BW8APJvokY4RT2NUALgNwHYB/ApjDGHvzAJx7D4Ba23INeDzaMQshSzFtgWZA9J9KDM1FoOjLAADqE5uS1hJYJTWYy8uWLUNaH/wgcNJWN5M/mEQoc+8OADjlUq5mTMQiBEu+g1Apt9hlUvx8VJfNsNfB/Hjfx3ydygf2uiFW6Zo8Bgfsbj0RAhgYVJEiGMouvGqAwimi6IxTzO38z+3jFqeAYLkptZLsO7tV7gmcE5IQ45030QCloRfJTR1Waqf9sDZSR3zi2+wEyf4dqcMjnrbV1Z+H5hP4RTXJjBvTtAROLS3EulOmmtsfnjqKW8aO4dqU5/zqPc+6TD699IhCT9EoULUVVNkMAv7uuVFy3mjIY/k4EI1GUVdnJd5QSh2WsIqKCtNNKUkS9u17AZQqWL36a9iy5WcQRdFD3uzwe51EmfcL5dUhnHHVJBCBQNQtdppKIekELt41uAL8+yRjemHwlxhjrYyx/2OMPc8Yyy1ApH8sAzCOEDKaEBIA8HkALxygYx+REG1kTArPhxQ5E3L0PH140LcxCkHkM32/mDGVKRhG/WtlGhazSElQP4dhvbLOe8n/m43jzrQ4st2kvOF9Lu6n6S+Pusty+UwpnYAwpRhVVoNnvnESvjDH32+fx+GDnWgYnxVRQyjLJMAOCr3cT/dy7I7XO7b5Bqz7QNrMy2uZljEQdJV1Zm0vCFYnXEmLQGDNnMMsgALoJFKjaPvTWrT/dT2o7vYsONlyqzoEW4m3987YyJU9xlfVa1raMXLE130HB02TkMlw8pZO80zokG4Zm1oQxuhwECDETGI4FtHrI2WxZk/3YbiSPAYKxhiS+uvHqOXGNzIahYhzomQQrmuuuQaFhYW+24LBIJLJJF599VUAQE/Pu1i/4TvYuu1es60kSWZ73+tSvH2PMY5S23sq6pqcmkqh+ewzGJCLm/ITQsis/psNDIwxFcCNAF4DsBHAM4yx9Qf6PEcSRNn2QJMQpOBxEAO6CrlJiqwHaW3nEs8x0loCM9VRvscnEDBqegVOvkifqZguS+uYQ0cXgxCC6393OibMdZZMUjN8IDFejoyuDxOZOxe7u3cgzBgQKsGc0WWeuIA8Dj/8fpG5mViOWUb8t1/Z8SY+bHmeH0/X/1Ey7Vn3+n/1u3HKUl44mGjOAH4Cgp3rs2sGyQErOPcMZSpgs4yVU6uDz+y2YtY6/ncTP3bQIpisH8vYw0t2YENjD6756zKHy9L9hZ02fw0ikZEePSQA3P2r8EmOqlgEo2H+dPxr9nhO8oSjX/R13n1vYdRtL+fc/q6XNvTfKI/DjtjO7dhbo+fXiVusDUZ92vOHoKfHqmVsjBGSJHl0Duvr+WQuFoshHrfCFCjl7/Hu3Y+Y6zo7O1FfX4+Yj+gyAN/i4YZ+pp2MGVnbVGNQM4OzJFlWMkaIGaR0KjghqyeErCCErCSErDgQJ2eMvcIYG88Yq2OM3X0gjnkkw24ZY5rbYmBsszrz7ow3oYGBQcjS4RMiYOysStNMS8xj8jfKcE8C/OENumY7XS38hcgkEvr+fL/yH96Ot5s+QocogoS91oQ8BgfCzArUJyAIFF6JgLh/uTiCNMq0MlGafeb6aGM7tiVdOl42Mhbr9hI55kOYCljILP4LWPFiANDzuhWIS2N6zJdKUbRQt87ayFhRka3k2FCeRTqmMorbn1uDtza1YEOTNaC4K1BIEne9+7tNCBgTAUhQVYschkQBskAggoAJBIp6dFvGdndwAp1rbFx5XovwiMCWT17DrhFnAwC2UW4lv/q/HwRNqZAqwvjzi4/j/vvvN9sbZEwURQ8Z++ijj3zP4VeD2Ygn2y76626yjHesM4SknWSMv8sb3m+E4pM0NBjQl2XsE/3/CwFMAHAeeOzYpfr/eRxgSLLdXeQOJPbWlKRZJCkKmX92HIFgzhDmXjDaVqcSOOmiOsxY6HQteq1bfPnDv/8NAKCBv3Bf3fRD6yoj/i7SPA4/Spkzjo+IQ7AeNVlaOyFij3OFEDLpUF/WHqE9BXGXM+NJJio0TeQxY37yLPqBR+8527pWEAhZyJifqwICQWAUHzTstGDy5B1QR0SROqsaiu6GHFkeRUh/99xq/AbKyz+H9nZOHP0sYwZEsQCq5s0uFQkBBGKWhDraEc84f9ds5Oyimf5JS3kMLuxc8qL5eXK0HXIojPKaWrAMdVihDdgtY8Y4MmJE36Ersuw3duhxylm0DNVOr8XMJGPUS8aWv9IA1YfADQb0RcYIADDGtvn9HaLrO6Zg11wqGWEFD78+kyCc0i0I9pqAWYqJh0T/4HlCJPOhHDKqCPZYsZlneV8U70SF75uK8cHGsGBs6thktghE85axwYoPmp83P2/sWgpAQEFZbuSZuCYHBKLZPZIsQelbEykElrdD3uiMC5KIAlUNgoD4aggZHa/IAliz+iysXnUOACCRSiCdjmBf01gIECAP059zH62y0PhSiLrWmN1NuSIwB+qkEh4cZojWUoZokFuBu5N8EBlSbcnFFLJuvL+kG7/97W8BZLOM6d8FCSIe93aPIgFA+LmOBUy/czHO/tW75vKTH/vLCKTzAfxHBEL1PPOe0V7EmrdDSSXBNIrUpg6kNcvybUxU7GTMkJgYPtxJvC+//HLz87nnnuurzyeK/F3TiP9zklrvtaybZEz1uikBOCxj21YcqBD4fx99kbFKQsgt2f4O2RUeS7ANGhVVVmHkRxYKiCb0OpT6TCFY/A0PGRNDc/o8fFu6FYIkoPeNN9B65x0OtmVkRqbqN6PjyScd68w2nsfF+YIs2bkHpGxUn9eQx+HD0PGWwnWP0o7qpg9RUdG/4CsASLI7s1DsV9Pi1I83OZaNx1skDEQPq6dMxedTp+DS9Ilmu1OUCSimEURYEN3dQ9HTY6XJf/LxJdiy5SQIICicz616aksCbhBJgDyUkzVBsJ7TtE9hcY0xhHXLWHeSDwiTT+QJAKUS8ACuNwldT0+PLxkrKeGTEFVtRlfXx4jFnEkORomnXKsVHA3Y3GxZRNvj/u7w7kx2F3cegwMa1TByl17RBW+b6xMrOZFZ17rVXPfXv/4Vzc3NDjelQcZCrqztyZOtgjsTJ04Eo14yZiXx8GNE9Tjmof/vBLON0up8//0sY3YCFrNlUfZ2DB5plb7ImAigAEBhlr88DjCCUStGq2pkBU5Yfg9mrvwVPrl6pZkEJgi65YlEzG49qeqdno2cTVOdlq6OdBMojUEQCfbc+C2Q+tWwW8YAoOPRR7Fj0SI03/VTaLE4Wna63C3ETc6cA4uoBREpdQb95zF4ECwoNj/vim/EpM1PQg555Rv8EAgUI1h8vbWCiFDT/PlJ7/XOWt0SDiplzkRGwst0qUxFAUIosblQR9JKXJY5CWIf3RMBgBzLFpWVZVHM0ScbGmV4eS3PFE7rAcEnlnLL2G01IkJImxmZjz32GCilGDVqFABg5YrzsHbtmZ6BZlM9d90zRtHevgQC4xUrjlVli5Dsn7G7pderoJ7H4MLr/3sPWip5Dp/SbREvLWbFfhrYtWsXHnzwQaiqarooDTIWDNrK6116qeMckUgEzCdkwdKB5ecovWgcau6ZB6nUet/aHnHm/Qk+Afz2+Of171n6YkPHWH3i4UZfvVkTY+wuxthP/P4O2RUeQwhG+IAkBYKY+ZnPoUhpQWn3VsiijCKlAFLkbNQ1t+P4T+/lfngSwHv7/oHXGx/Tj2A9fJLrp6WMQgyMgRFLGU53YFytoT9WBKW5Gc2/uMdsH3v7LQyrsx7Uky6ug9sUUpi2Xq5fpurQjShKwv5laPI4/LBbOs0OMpxbDVEGgAh2K5qATIJ3epkmL8NIueKq/tXmljAgICBQqdNisrTFik0RXM9bmFnB3tPVUR7LbS4Q4EMcba7DlO42K9KTXKZGnLplXV1d0DQNYZk/+7FYObo6qz1kjOkTo917HsWq1Vejq5NrbNFjlI2FbWSsKGQNjOt6vFbNPAYXSlZtRDLsFFwPF1ljgwwv0f7www9N65jhupRlGRdffDEKCwsxYYKzoowsy75k7HOf+ww/hs97G56uSzx1pBBftg+J1dx7ZFjGlr/4nNnWPpY57q0qt8nooUC/MWN5HDpIsozvPv0Svv34s5ACAYxb8h7GfchLhwgMkIJTQSCgqNfQ95LRlNyGpBEwzCiIxP3y7ke3JFAJQALaLR95URSQo59FsPAKaJ3O7E0hHEbVKEuZfdbZI2E8LuHCUoBEEFFFJMZzV9GMlvdQQ9pQXZKb2yuPQw9nHUhdDT9Hy5inDiSRLP0u16b3Onpx08ZdEHdabqote51kLNZbDgKCDHVaRnbGN0Aawwmi6nqKF2ammZ9LWVQPxPKi9LLxvusBoAy2GBN995gtPT5haGHpRE/SzXnGvTLGoCYVsI3OpAT7rJ/vzoljIrGD30umFUSh2Nd2bJEPVaPY2hJzkLGvnjIaqXOGgxbJwDGsu3YkoLe3HcUvfopYwXBomc3m+i/f91sQI/744ol9HmOXrke5e/duTJ8+Hd/97nfN0kd33nkn7rzzTgA8ZMGNmpoqBAIBaD5krOhM7v0Jji9F57NbTFkbg4xt+sCKWQwXBlA3yyKUxUPCuOEPZyAUHTzGg77I2Jl9bMvjEEAsKoJUxlXyW8bzGDJmcxUS0cn2iVAIQapGTOlyyAPMVsYgofYCEBCxcaWOHhFiYDyIUAityzlYprdu8wyyp1zCB7lkbycADYRRbLvlQgBAUJ/xVxb2X+cwj8MDOxkLIIqdlYBWvp8JFyyd1eV2xUf1+NfaJsibrGdq8W5LKHLLlrnYtIkXkverIkETvFNOEKckhtttmc0yFp1d5Vhua7Vc9rfhLtsBuKM9bbPiJXQNIjO+zRgEmEXGNE3zWAPclrF0Rp/06PcnCiJISkN374Eo63vk4N5XN2Hh/e+isdsi3TNm8lAGoUeB2JbOq/APMnzw+nN4858PAwB+/MP5AICWIbOhxF8CACz4ynUoKC0DTaoAAZjk/x7W1nLx8KIiPql3W8Pc8IsZS6X2cuFXHzImV0UBW2woANCUis59VlhC05Z6/N8v7wbVNGSSFtnrbhl87vGsZIwx1n+13DwOGUQzrd9GxohFfOTohRBDJwAQ0JLaCckmkjeSVnJXJhEQf+qv5vr2buvn3329LR4IQOsDD0D5472OdY5yTSwNwiiea+ICj0HG8H351v28uzwOBYhN7ydWKOI/r5UwfXyuNUSdHa6W2Wqtc/XFgaUtCKx2WlrXb7YsUl2dQ6Fp3HLEbJ3s6hR35TFd/qGCOkNTBXd3JQBC1Fuz1Y6r5DOwceM8tDSPBgBEkcCysasdt2VXxU9kVBAA393MpTwkPYvLsIxRSqESzeNCNSxjRlHyZHKn4/6U1OCqg3eo8JcPGgAAzT0Wsb6vYZ+jTcxHmT+Pw4f/z951x9lRle3nTLll793eN2VTSe9dCITeiyBKEYVPUAGliDQVQSkqCioqKM0IEpAWWiAQIJAe0nvZlK3Zzfa7t987M+f740y9M3ezgUA2y3348cvMmTNt78yc57zleds33oj6/fcimAjiuvcVBHIGW7a7fcxyTWMyqJtg/vz5jscZNGgQZDmC4uJ58HoDltqTTgh0bbC1SVIQoiimzaYkHLEIvyoxWa8QAwBv/PF+7FmzEoEWZ52y3oSeRcBmcNQx2McsZD6eKRbPXHUvzIrkvGsICOFAwEGhMiZKRjkYDgQUCrKzgPDbRsWpqUMNgUsatc8UpA/fwYlLb8PVv2cDNpciIUCgYGeUmaA9lGJhcMgXvMsMvlS4CM5JTMJEaRAK+FysunABBg4Yfej9AHvyBnHrkhY2Nbqk3WTGtxqDsUZstnYss/RpVJhLD6qlqohaC5jbAvoJQenNU7q97CzeA4DDrl0nYMXy77Dzm90hBEiYLGPhuMzkX9T7FTQLc0rRcg6cJQM0K4u5e1csvzzlCth+DfXPdHudfQFOsh1aPJ5Zv21D0OqqjWQyKnsVflFShD8V5mPJupcBAOsm/9yyXRNxVWIS9onppSF27dqF9vbl8Hj3YvCQdd2eMxTahYMH37a1y3IEgiBAPC4XJT+ZaN+RJ5BNGZE0JoHjjXExEugEALz+u3tRUNGz+NijhQwZO0ZQSeowbuuTmPB/p2HUzh3IirWCU799hGMuzOKWDQA4yFRGzBRsTUCgUAW0xToj9QnqANlNbUFBjsEVbkWivh5CysxG4j2Q1bgBAmDyqGEOR8igt0DO4VChFGCqNBQggC+v5/VDtZgx0XcRXP5vA4SgPMmeJy85PJO/VgC8PqXGZeAgOx41Derlch4GyOz5TrVGEULA5xxCwZ0nGJBVajlv1Z6H8N6oBP46ciCrF2k6X0JWLOWhODUpJpVm8JRDLjXi7TRXjJmaynJUVxV3ShzoS1AUil+9uTXt9nc2N6bdFuml5Wm+TgjEA0imuAnfePNRJNWqE5Qak6ny40YBAJSoBLkbw3QwGITx5nQfgr5+w5X6cuXAH4GopfoCXRvQ1taG7Xt3otNl/87QhAw5bFx3+yu7MWzaDFu/zqZG1Gx4AiNn9t5s/wwZO0ZQdtONGDZ7CPLOYdkl/f72GARtRq/O4j2xdoAwyxhPrWrlFIqtRnLn3GfV/bt/DPacehr2nnY6hJSC0s15LE7mty1teEmag0unDnDaPYNeAl+u4dZ2EljsDlT9VPCuIeDE/gB4cCqJIQ7Ft7s9FtU0t9IQFBM5Ojc5BWcm2YyYo6mWsTTHVxTsXrUMVFGghJJDHovRAAAgAElEQVTggqpGkmLs3779cvTziAAB3ltndSHyJguw5qZEyrlloliSGlwuF3w+q9hyfcML+rKZjPVFt9yelhDmra49ZL/8OYbFPjGZkexwH/x7HEsIhltwwksnYPLzk5GQGOnKD1L87A0FgZxBAAApyqzY5cNHIK+UERolKgGi8Q7cdddduOCCC/T1888/H1pVRZLGzaghmTTCGoYOvR1zTmLEvqlpPkSRWb42b96M6upqy36uCj+S9UYyTbIhhOy8Iow79UzbOZr27sZJV3Qft3Y0kSFjxwjEsjJU/O4hcGqgcM7pp8Pl06xfqtmYEwBwUKgCgZqmLBpnSz1oKFVuoHt0PvOsZb2uiJ33m6EwHpG+jfH9e49mSwZ2+PPM1tLDQ2o2JafIGJDFXBRu7+ERO43Y0BSLLK9mWKVTqbe7KZ0Pv2XxIrz9599j80cLQeOy6dpT4rw4DpCoLYBcMGVpCurLk5qsQEHhGmjEtIUW1FiKHgNAIt4MqtbtNJOx+96y6iL1BfT0efKbEnyo+nd+a1MaHbgMvnS0Rlvx20V3YNpuBWXtFFNemAqiUFy2hD2vgdyhrKPq2veo8WJKQkaiuguJNsNa5fF44PUa3xiv16tP+tJq/akoLTlPXyaEgOOM8cubxcapZcuWYe7cuVbRZYfkASUu44TvXOV4Hl7svZSn915ZBoeEwFkLfYvJMPI690KBbBm4tBgdTrbOQDmHAs/PPXURqsqdzydvMgKfBe8piPHV+noEbpTnZmQtejMIbypEf5h6VzRluM2hQ3F6GStf6/PHnXZJf6w0ljEt8JY6KNznf+s4m5syNY4t57SBKLp2nB4n0tXKdIfMZKyz08i0dJHUu2LgTW5Knji7WQgIqCnwnwSMd4nnGUnz+YaD4xj5MJOxzkjfy6i0lbFNg6qoKb7Hzwbc9TUd6bpn8CXjb09cg4lPrcbtryl47F8yCKV4+FkZJ29mz3Zj5QBQmsTks1hs6ek/+ikAQFFdgzTFgT94sBHsP3DgQCimUkmplmMzCLFrlQ0bdhcAQOCt74uZjNnrJ7NatVm5eRYtNHP/GRcOwSV3dB9rejSQIWPHMERVp4IqYYzePhdjBoQgyElbmSTtdQnkDQcAzJ+lkjMTGeMKC3DdT3m8s+8d/Or7zmrZHFXAuycAAARxJEJilb4tDI/jPhn0HnAmMkY45984PawfPY/iA69nGvYclUX1UBQOIuXTE0KHZvewXJtlbNX8lywq2zmnVcIzLM8oh+JA6qjJVelO4zoxXxavvkuU2j/6yYaQqR+HsRJz0w8f9j8AwI6dd6G+4XkAQGnJuY7H7ytwGhTTdAQAiIQALh6UAGV5Xgy6awEeXrgTH27v/VlvfQGUUryw4XGcMW8PJu81Hsj//V5GJZvDYO/MU5HAaMQD/8aat14BAPjzVYmlpFqWb3yh5bhmiRdFCUOWmbVYFMtRVpY+XktW4vD5huPUU4y6rsVFZwAAXG7re/zee+91f2+q2zva5ez5mXr2oF6lvK8hQ8aOYQTD1WyBRjDixIHo//sH4c7OQ6XPmiGnZYT5Qw1wjxyJF09iPztRTc+D97+DN07PRsCvaikRgsVXjbGdjygyBO/JcOfeAPAeJARgXgMLul5w0+wv4xYzOIIoHTxUX3Z5SrrpaQcHaw03TpFAVGuPkhrL1Q0uHrkAlHJwQ4RCZfgLCu2dVI6Uc5qRYCDkeWzZvHvXrUZLzX7b7hox0Mie2aJmvtb6/X9yvMaukHkmbpW2MGBlVAJ4VCgs41lR7FHNPGeO1+t7bIzrMRlj/xyf59d2xPtb2Tfk8U/24trn1qI1dHiW1gwOH3tatuL3m59AQSh9n3EnnsQWqNFJe7eUGBs7tNDkiooKpGLJ0kl6WTCe716CRlHi4DhrMo4osqQYt9vqwdmwYQOCwSDef/99x3cp8K79mwAAgmgcnyq9L6EmQ8aOYZgHp4oHHoBQWIic48Ygz20daDl1dp/TVYuOi08ECMET57Ah6pRPbsTgmveQrLUG3z7RfxfcaikKDYQqTD6D86jrwLhEAhfFf4vhJZlypb0dLq+R/XeYMffw8OsxYtc8fZ1XJL026eFwCzcXA6UEChRQKHqcmBmRYhaHYhZzBOzSKnFVvb/s7ukou8MoHKyRMG3gSJrKhFHFsAh2ti445PVqZY1SpS1Sb1kAp1vuJMnBdWKKj/u6is7L5V7dMqZzNwfh3qTc+wbKvoYPt83Ht5Z2/3fe35kPmibRJ7q1FQDgymZjwWWXXaZvu+CCC3DFFakSL92jvX05YjFrtr/m7s9yiH555513sHLlSjQkmRkv+9SB8IzIBwDEdjm7vbXC4R1NB/Do5Rdg96pljv2OFjJk7BiGP9+eGZIzeizaYtZgSVGVueCpgn/sfBoAsGKU9SP4+vH2RyG8YKG+/N2f83j8HOsM5azWKLYog7CRDoOrh0WbM+gdSC3yfihwhKJf43JjXZH0AZWaPiMrm7tSd7XAJ0agmUcoVSCILrTyjZByDMLUVdGFit9+A8STMps2idYqVEZEYucSct0QCtigoCgyls6bCwCo3rQeAFDLt5r2M1chOHTiwe7dPSvDK1AegnpsWVbAcSm1Kk2EcMnulh4d81hCT6x91ES87hjMAlNJ0k4I4g5tGRw5xONBvL3uZXx7Gfs7txYTjNy2FQPnztX7JMRsbNvNgcrGszp69skAgNjuDoTUYtuBaBc8Ho9J2gWYPHkyBg9OE3isorV1MT76eCiiUSauTGkCyWSbpQ/HCeA4L0aOHGTbX697qX7H+GwRntEOVnYVo06YA0WWQSnVrek7ln2atv/RQGYEPYZBxLG2Nn9ZOda3LWLb1dm85qYhioKEaoiIuwhePNH4+ZMCwbONB7Flv2Ehe/YMY3tCJAh5rDovC/MvwUWJ+/GDE6wKzRn0Xrxb/xRWNL/5OQrPWvfg1VkmiNUytra++2BsLx8DQFCq5Okf0lVt76BtQqfeZ+eKT8G5eJviCuGBycnBOCUxFm1JpluVGneWMIkXt9ZW286vmCxjYg/IWCyuTmxSTIk23TFw8IK5Qbq6usDzVqsepTKQdwhNtGMY5t8hOTYPsZMc4oNUMpbFc5iUk74makzK6I59mXj14z9j2m72e9UMOA1bRz8ISQZ8M2dg5PZtGPCvf6LlsnsBAIpsvM+nXXcjACDZZGQNRxNx+P12MVVJsk/KotF63UK8afO1AIDOzjXo7Fyb9lo5zgVRtH+tIhEmHBxUY9LAEfimGc+cWXvsojt+jYKK/ur9yLoobGPVzrTnPRrIkLFjGKOO729rK6nMRXuSDWwXJqZhojRILyNDqIJOn/FgLxtjLF8cDOGHnX/FuXmGQv/KkdaXIOE24oaG7p2PXz/0AHY9eB5+de6oI3NDGXzpCCbbURfe6RiQ3hMM2fcGRux6AZySRLhtIEAASTFcjclu6gwmJhfCjyBOS4zHScnRoFRBW30twh3tqNlslEJpratB7dbNkDqssUNKWMJkeQiGKKWQ1XhHWbJaa52SAojpXqmFjCUgDUif4WU5Rgr9qlDyLesCePgos4aFQiHbLJ9SBVyaGn7HMtrDCQy6awGueuYzvU3JFgGPQ4KISsZGZLG/0+JpzppPsYxl7IihoylseyfqpbAuXVEz8AwoJBfvPbEZTfsCIBwH/0knIZrdDwAgqgr7F9/9G4hu9rtRk0hvIpnQi36bIUnW4PlYrA4rVp6E2tqnLO3bd/wcsTibWAmCPaie40QAdnLe2KiJCKuGBo6z1KrteHU3Tr/uJ+B4AZXjJoITGAFTZAm8muAT7uxdWbwZMnYMo/+oYltbYYUfoIw0FdFspraugqMKakqAj2vrMSCZRMRU07tA8uDduy/CGz+djUW1zAQd9hL86ioefzuPw515V+GFG5bg+BV3Y9yWf6Ky7kMU+t0QeK7nmVQZ9BoQHJ68gvY5H1S7CP0aV4BTkgg0sEQR2URwOC79J2UoqYIICcVKDgTwlrqU+zday6WEAx0QitNLpWhkLHV2q0h2uZbvxU80tpuyKQksns/uQShuvvlm3HDDDbiu9Hz0U4P1NWgxYyIv6rN2M1paFgJK35O0eHcLGxQbA6YEjzQF3FNHm1F+5983mlHkPyLY8vFGPHvrtdjwwRa9LbB7O7aueUdf71QnCHU7OvDaw8Y7mFvCLJcF5czCNGD0OOPA6vdehoKqqipIkoRkshOybDz3SQfLGAB0dK5GMtlpaROFPADA2LGP2fozJf70z4OWMc2lkH8lnMT4087CrfPegOByWTKsU+U4egsyZOwYhuhx29q6E7VrzVZwXaALxbKC42rOwukJZuLd2Q+g8gCU53oh8hz+l3UTHj3IYgV29ydYOo7DiRPOgd+XjwmbVmHy73+Kyuef+3JuKoOvBAJ/aLV0K1LcdIQHQJibElaCkw4zCYs509zmFBQFA05w7Csl4nAPzHHcBrAZLgB8+ry15mOqpQwARAgYJw1Uz5kiXlsTtvXX8MshRtwLAZDry0FJSQkExW710bTMvG43og51XgGAF/qexUfkHX7xNGRMixnzOO1jwuVPrfrC15UBsOLVJwEliOpNa/S2Axdcgl+8bDyHgytLLfs07GbWos7mCHJL4mjYyZTwzaXwNFmLvTwLuG9pacGSpVOwctUZeh9FtmZfayBERCxuDdRvbfsIAMBzdnkkjohpkwgAQFIndMSV8k6mPIOaa1KWJMiJwxSp/oqQIWPHMFyew4tBKQnIaA+PxvjYU3jgV3/C/Tftx23X8njgch5Tpt2h9/vprfdCkU7AelP82MCBzApCCIF/9mxkTZtmO34Gxw4EBL/Q/m0FTPqEEGohON0ZSQWiqdEbnYJtzlm4yRRC88h3zgPJMgL6lTT1VJ20xQBgsjQE05PDUFJcbd1QblhnEhMLkF/uQ2wOiz05j76hbxtOKnDg1yvYSjfZfvFkAptM4shmcHzvnJF/EQgOpkVNWT8xqQDxGSbrvUbGemyOzOCLINTGvt+adzyRtLr9By/6EC211u/AG49uQLA9hlB7DB6v86SCJtk7xg+1vrvxuFF/VDFZgX2+4foyIQI4Yk3M0YRhvV57OT3Cid2WbpO02rEpVTtICuHnBcMyJiV7p4U681YcwxBc6bVbtnUst7XtL6X4yU9fxIaHLoXfzfZ969YNWPP9NZh94ml6P44jmPbT57D1ys14Zub9uGf4FYfhz8ngWMARoQVUAQigmGKyurN5iCoZs5RWIs4TisX/eQqbP1yI4lsmYEn0dQCA+3xDsoVTP665JdaZvSxZP9zLDzJCJYLHKLk/CGclUlyFQcaUYg/GnTwQcLNj79v3sL7NnzTiYqiDNoWgunXi3Xzo+6IzX06JR4pPL9L/fkqJFzTPZWRRutk35KHhRqwrcTt/V0bcu9CxPYOeg6jvFl9Xh6Y1S7Fixf9QXzEbrQVj0FlM0R5zjpdc/34Ngu0x1Gx81raNKhSh5SypxTu2SG21T04UhRGsmTMWWQSPW1oWQjEVJBeEHHi9zGotinm243CcqAvHOoEf6APx8HANsBLD1HdUE7mmitJryVj3SmwZ9GrwIgfBewI4odK2zWmwHTR+JoqyUwKPeRHg7QGYBdlZKMiuBFCJ6bjoCF1xBkcbpWhGcR0QKLfHGx4OOCrDL7tAeKvrL124EADwnN0yRojd1a5h0VN/R+DCJkQom70T0XBF7Eoy2YrC/gMt+2iWsYKK/mg/UI/6yC7j2kCQ+mZYChgTp2FF28SuObS60VEoLDVmxfkgfc8yVp6bIuHhkDFKVKuF4mXDzeAsN9ralyHQuRbxsTPhWtdm2ycel6EoSrcxiBl0D47PgiwlUNfpxZCrfohSAB/P+QcAYGrLk5j/yHoo0gGIwip888778eofWBLN1k8bLMf54RNz9eVErREL5lJdl5deWogmtXCCLMfA8x7dMsZxLjXuy4DmduT5LLhchYhEawDA1g8AQqGdCIV2IifnTHR12YWqqY9Hv/u+YWt39beSM3PMmNlNmYhGLPqLRxOZJ/0YBscRCJ7pEDzWNHJOqARx+GlHDMu4Fr/uECFjYHvwCwexemLtOC5WiFR+053clEAkdAWKrTUm01jGNDTt22O4IEx8JxxtBwDsW7/G0j8eYmrh7iz7rJ8DQThkDbyn1Oq6Wdbh7L7lOpl8S2DBPlBZ0QUmpySHYKhcCuI+NBlTTFode1u6kT4/hmBzU3bjp6YmN/PGjd/H/uq/6S5NJ7TFemdsT2/Dspeew9q3X7e1axaoiLQLScGaLOH/Pqv7mAi+hHBHNYJtuy3b5WSNvpxdwCxglFK0/HOz3p5IMMJFOOOdWbmKeVgUqpExty3BK5k0shgjkf1obGSllkiqlo0J+QUNju07d6aRp0j5EGlkbM3br1ssY2venp/2nF81MmTsGAYhBHOuHIHLfjXd2s7lgqT45QlfBMFJyjiDrxUE1aojf0GR3uF7XmGkKiVmTOmGjPFQsGfvtBQ3pX02bEZn0wFobE+hRnB+3JSxaI4Te/ORBwEAOcXGLLoxso+dCgR79061HD/KmUgbIYiluQFNHoYqFJApOB+77knyYJycHAsuhYxFInYBygiMc536SO8SnPy8CDokTEzg9+JB+nN7ZyeXpPrnpi77ttZohoz1BKvnv4xP/2t1KcqSAqow9x6Vm7H0hD8h6Dfcw2tXaa4/9hwnImEMn2q8M3LMQfsr5d2Ix9lExu3KNbU1oq7+Od1NyUocWclYWH0fzdmXnxeBQACKqbRRyU8msmMHra5Iok4aNn2wAHLSeK7yStPXy/yqkSFjxzjGzO6H/JSyMUX9c22zESq3Aq70LqEMvh5QtODqnrjVuoEgMfFWAuskNJawave4zvBB8bOJAYECqvAWMubkmjBDSiSQiLHMrOqthhaZubxQMh5H+4F6tNRWIxZis/Rh02dh/KmsnJdsInE5ocHYucOUwZnGMPPHEVYNP/2aFQoqU5CUrGXitk5+1q09BxyXMvnpg0FjD39UZWv7JrcIlTDqAyp+AVQgACFYP2u0rT8AUIcs8PYMGTssaBUnAKClpgklnkp8Z/CdENW6qGum3g1FbgdVwgi1M7JUOoRZfN/7x6PgueX43kOay49NcAaOm6gfU2oxBfRzBIlEAoQQuFzWrOfdu39jcVOmWuGrqh44/JtT41Jnz2Y1kK+55hp90/bt2/VlzT0Z3dwKMzjO+N5JJjJWNMAe4nO0kCFjfRCcKKI5apiZVzS/CVf25XBVDjp6F5VBr8CK2X68MIfDwREFh+5sAknNVqIKDGkLg2XE4u36spLvgmLyLRJKQdWSQUl15pzqpnTnXo+cYqPocG5pGWJBFqey/PV5cEK0K4B/3/pjPHf7T/Q2f34Bxp5yOgBYBgOOErS0GBUjSMI5SmxmbhoxWIUFBxOeA19gxEtpMWNDZFOSAdd3FfcBQFEo9tQGbO2Exiy8M/GNEsRPYTIheWJKmLKa6kf99vDllkimYPjh4PXf36cvR8MRnFzO6kUOyBqhx2kluuYiHviX3s/sGdz4/tvILvBg4JgCEJ65Js+64RZ9+8G/GGSv7LYpiMfjcLlcjhYuCxlT3aUlxWdb+mRl9bxyi/aNOfXUU3HfffehstIgUa+++uoh9zfHHsomN6VWr7I3IEPG+iACzXE0Rffo652JZhC+CDndiGhm8PVAyKXgzVkc3GLPlOc1OJExCtXYY9pk/rRJQ7ORgGiJI9KU/3UyBquFjnBe5JcbH9rG3UZMiNlNacZH//6nra3/qLEoH8YU3nOKjWQFLsU8ReLOH+PUCizm/WhMAniC0psn6W18HrM+zEkaJcqmTH7RepA+Jo6cSCPxwafGIxKi33tqEQKa40JiQgGSY6yJRQDw6xc329oysEPk3BCIC1R113W1NOP1Bw0SxREB8cDTjvvGw9ZMxbb6Okw/fwhyCpmrX4sXU+LGu5f/7eMgFHrx2WefIR6PY+++P9mOS5U4CBFACM9KgQFwuYssfYYNvVNfHjL4Vsu2g/EkZEoxdcpr7B44+3s6ZswYffn555/HSy+95HiPgDXLOthmWM16S/A+kCFjfRLRrn2WdebS4ZBdYBfVy+DrhdlJFiMxxu/sLkoHLjVVnMoACNMZM0lbaOEb8VnFUAo9SMIFaXgOKE+QlxXQLWNGgon9ExQLOwe3p0s6qN++Ne11+/ILIJjKNXEp55NLnCcovC2vMoXE8RwIbxyLcwtwH5dvIW0ez1D0ZcSS1gFSC8Yn3Sim84RAUaykWinzAiKH5LBsmOq4oyvjpuwRLq68BRcOvBGEY3GK69770LI9KocAGrW49gHglKuGoaPRGhg/97brkVciwJudQG4xk41p/fdWHLh3pd6Hc/N6oe50+cfVNU+AqpMnI3vSOgF0uQ0rckmJYTVrT0qYsGIbZq7agdzciRCEHHCcfSJ2/vnnAwCmTJmCvXv3YufOnVAUBd6JxRarNQCUDDbexZ3LP4Xb58O3f/0QCvvZtc2OFjJkrA+Cyo2WdQUKZlww5ChdTQa9Cedf8S88qlyCk8/64WHtZ7OMgeo6Y+YtcYXoPQCAEg5KsQfx0yogCopejqg6xAiUObZRG0wSaRTsUzF06gwATK0/FS/cuwrB9hh4QYQvZqS5a2RJllWLnEPgOAB4uNT7TQFP2P/acXNdiO+2xsvV1hqiyQS39LmYsbipDqnUPwuJWcwCKSebHfvPyvOBJ8SiG3Wc0KIvy0NzkJha5LRrBoeAwLlA+Bw88p3zsO2T9wCwOrSAEe8oRRbp/WdcMBjlQ53jNTe89xaiXZ3IymW6X7Fd1ueayhTBIIvNLC6use2fCq0QeCCwwdKemzPBuH4hB3FFwT1V9WiIMTdiXczIyOQ4O+nzeDxwuVy6xAYAhMNhcC7eUj8TAPLL+1nW3Vl+DBgz/pDX/lUiQ8a+BqCUYtq5fXuWnkHPkJ9fgNOvuQ+CcHgSg9ThS1HVuVkN4DdYxkur1XgMApTRA7g09DIAwEeDKEETZkQmABfnYXPHpwBJmSnnXA7ALtyaDqNPPCXtts6DEWxffgB8ShFjzTK2YvkVqKsdk5YgeUgqGUuxjBErkeREe0KENmABwNq1e2zbj3UkTGRM7u8DVTNM+TSWsak57Pfeu+9Rve26rM8sfag3I335eeGljDTFw+xfTelek4yQE9v0vlPOGoRnbr4OADBq9smW4yx/+b+IBAI6GbOdZ3QhYmpSzYwZkxz7mKHJXPiyDIPAwIHXAgD8/pHgeT9crgLMP9iBp+pb8csqq7WO41zgiPMzxfM8ZFM2dTKZBBE50JRYUEIIxswxhM0Fh+LmRxsZMtYHMXzGiZZ1pTvxpwwy6AH2zCjHWzOshKQtflCVtjDAhZg74UY8it/hNpwU2IoX6CV4Eldj58Y5KFbyIPOsj8t3LvwFRoavphhuTj3vDnwaQjnhLBZ/QhUKXhCwqWCFcX1mGQ6Ft8RxmeOZDmUZU5IpH3uRQ86ZgwAAP77iB5Ztwa5C5p7tY5axpGwVzNXgUovQ3+x+HX8daYjyCurfuq31Y72NR4pV02RtpCKH1njGVdlTnFJ+hWWdJ2yCUOi2yzc8evn5+vKA0eNw64tvWrbHI2FHMuabVQ4icDoZE10GqZk182NLXy1g3+1i7sjCwhNx4uy1GDzoJgwbysrvzZi+AHNO2gRCeF0547OANY6NEBEFhQfhdtsTYlLJWDweB3HzoEkZNGXcO7jXyPyNBJ0LmR9NZMhYH8Q5P7nFsp6hYhl8UcguHv89hYdiGnQV3sO4jMMD5iNhuJBg7kwVlHIgIJC1ciiE11PsLeeS0pcrEYdmI1DOMvgWPO4cK6bxK0oBXhARlyPwH88yNM2XqigC3DQGqupf5Vsy/QyikUi4YYsZSy01IHAQ1fgzUS1skkwmISX/ho0bz1Kth32LjSUdKhEAgABGtk+ki3FhiTGga2RMMmXfdQWsljFzCQeSVPCzD3Ycqcvt88gSUuq88i5s5eswIne68w4q+o0cbZF+0I+Xm4tkizVTMu9cZt06eJBJ7oumCVFWViUmTzaC6JtbmLuU6u8SB1HMx5AhN4MQ+/liit0VSSlFNFoNUQzjsssLUF//gvUWeXP8GvDBBx+wouEUgJRaEsmgO7EMGcvgq4Dgss4gKO2dtbgyOPawbaBq3cgGdJ0xB5LBqbTH5TZmuZQScCAmN6SzZSsRY7FjpUOMAsMzL2EuTPf5pVi4QsuedNZKiwRZZt6O5QfQ1dKC/RvXQVFjTvbyTXo/ReFwI/6M+JxyxM7sh05TQLqWAQYA+/dPQYqhDFVrVurZawCzjGnlmnjVpytJkpqwwAEgtq9t6sz9WIPFMmZ6BnxgCRiSHIaH59Dfw6wnokq0JKlT76uof5RKj/rNSvkbLauxl0rKwICUxoo8LHsS/utZglXibtRz3f8NCyqYph7HW99Hd5YPNCXbmAgc9u/fj4ULWe1QQbC+g4IpSN/vHwXAeJecCJgZ/T12y5dZhHnfvj9i1+5fW4qQcxyH9nZDTmf//v1Qw1L1gub6/fgOL4P8q0aGjH0NoGRsYxl8QWjEYdVINqBuHEJYqUVCHUsg8WqMhze/3nQMZhmTJMMy5gTRdwbmXH0vTvquIexYNpQRs2jImNEScDj/todt+9duY4N9NJhENMiWNzQsQt7Fwyz9FEWACGMw8xHDSqdlnrndY9F8cAhSrVpt9bXY/JFRzJoIHIiaDMCro0F7ezs6OjrU4xFIQ6yWC7m7cgXHABKSabBTf8r/0G/DB2ZN0fSntOdDdJD2oOoQ5FEzU908h+nnGbFFSv0XV2nvywi1BbGB24vtfD32BjfBxXkxxD8eU4rOMPqQWNr9r/2bIXnxrV/+Fnll5fq66PbYAuEBYM8eI/6R46xk0G1yiY4b+ze2oGVxHkLaRXL4kEQdrGWKkkBn51p88ukEiGISdZffl5EAACAASURBVHV1lu1JNXuTprxfp17z427Pf7SRIWN9FPn9DA2W1JTmDDL4vFg0ieD7P+PRUEhAoNh0xjRo7kkqmWa7qmVs8X+eVPsIOP5bwyBknQ7Bc7yxLxGRXTQAcVNWpTebEZmYKSgehCCv1KqUnw7ExSNrYglc1Jj9ywpvCTYPm9xuVG33+U4FswCmuCkBfPj048a6QPQSSSTI3CafffYZdu1ihcop5QCBAzVVPpDVwae+I4Ip9y9CTZs1VsYJikIRl3qHUGXYHDen6YjBbF1kf4eAer3FLgH1DVbhXl51aZarsUcSpfh1/pOWPg+/n6b+YAZ45ubvYZ2rGivEXeCJgG9W3oRpKeKq7orsNHsDuSUGeRowZjz+7y/G3170eND5liGTlHcRm8yYE1eyshh5Gz+OCcm6XAWmbaqoK9EkT7q3jCWdyJiDlt2GjVejuuafkOUQ/P4m23ZJc4umHK5o4CA9A7s3IkPG+ij8+QMQSLC0cZpGCyaDDHoKGcbsNuomSPJM+JWk1KY0wNqUpKH3QykBoQRRLV6D8PDluSG4x0HwWj+Si57ZjtySUn3d42clVxr37LL0k5I9e7aL+leC8BxmSobrkyo8ONO7UQKTJIM2gaHaQHIICBz4fA9AADmQsGWrDho0GIOpNaNSG3ve3HgAbeEEXlpjneE74Z43t2LErxb2Chdn0OzWdZQIoaCUIqQOqCUuEfX1z1t6DEMVrqBz8ffRTOj3xPxsHDz4lh7HBwCPL96r3y+lFJE0YrNfN6Q+A27OKmCarbAYRpdskKBh02Z1e0wz0RIkEckmNkEo+/lU+Gcy4mV+tolqAff7j0t7zJEjHkT/flchP7/7czuFIDpZxrq6NoDn2HfFSX9MVlX1Uy1jAHDGj27q9hqOJjJ5xH0UuSVZWLz9JeS5S9KKZWaQQU8hpRD6cTUUXV6a1jKmw/KxJPDAnFLOw+VJ/wlqrTesavN+w4L1V75qVrXn0LTXWo4nu7AETvxMliWAA/rJhVptZMgKjyCMAPNf4D7ciGcAAC0tHwAADhz4FMBYm2UsFX/5/kWYfM6FGOEfB6UrAZfLZQks9np94CGDEoPYaW5KTh0AlR64LV9YzbTLYkkFXtcXqy/6RRFMsPuLzygG0haeN36MKTlZ2EqsvzcBcGVeM4pcApbPGIkSgeKzZQDlrH/xtlgS33xtA1yDs7EtkcDGb4xBmbv3yRN8ldj00X7Leks2h3IHo6kUMWKs/AUFuOTu36ClttriknSCkDTsxny+kfVszl7cs5eFCRCS/j32eMoxYsR93Z4LAJIOz/+6QARlQp4lzhAAOJ5dD3EgY42BZpQDjuzO5em9VWgylrE+Cn+eiLgSwcFo9dG+lAz6ACT1syyos3FRYq5IkiZmTG8ylTGZnRyBdWqGFQCACHB1oyv18XOGe4oQEaLtQ8ph5fy9+tp3f/9XnHfLg87HevafaG+oQ16/QkxNMs09UYwjCiOoNw/GB3931f0AAEVhbhri5lFx7ywUXMZKLB2M1tgGs/Xvvgki8ojt67QIUQLMKpiqv6VJzmgJhD2RoPGqSQLB2NGXfAhp7tJuRhFziIRP4KEoLH4pHh+KNZ9dyNp9zP01QIhgw2omyyONyLUc5/K5a1C3tRV7FlYDSQU10UzdytWv/9uy/plotbwqhP3tpa4EvlFyEQBgXPaJKOwqxbQLLsHw6d9AojGM+ruWQmozQgJOuOx7bP91htvcXG3CPMnQphaiaLgnp02dj1kzrVUAegLZ4fkPyTIqKi61tUcjTGyWI8bzNW7cOADAe5sWswYHcpeqO9ibkCFjfRSK3DviSjLoG5jMsbIhkmrFmXsaB4DqMbmJhHPGLjGJNboJh85Ei2krD5ene+tO+eg7UDTkNtZbSPmQEjfyywzXTOngodi/hQ0gJZX2OJm5t90AInIYrDDdI4FP2Ix6f6hU8JeSdaZzsB6+mWXgvAKyJpZge+VGNMdq0dnUiFTI7THIbTF0dlpn8rJiSD5o0DwwvMrGehLPr/U1q98fLYQ1N2WqzIcJlCrYevxYbJo1Cs0t70OW2aAfDkcRi+UgHvfqhaS377gDSVU1/qaSxyANMIhyVQ37e5IkhefjRhzsSh+U/nVBvKuh2+1aaEEz14kBPjaJSKxrR+Bdw6LWPo9Jh0S3GxmX0y+6FDc//zqS+0zxmSaYyVhR4clwu0rB80Y4Qk7OeD1ejFKKf9U1I5B0ritrhlPMGAFQqQrEmhHoYmr+RCVjZ511FgoKGCFU1AmAkyufEIJh02bhvFvuOuT1fNXIkLE+CsHlPnSnDDLoIQZyudiyv1a3jAW9gIvmgMUFEbzzzjuW/tpnkJgsY0Kk2GIpIYRAdFvJ2OX3WmPHOholEMKe5VjIqg3E8XnILcnC1Y88jqv+8BgAYOMi5sbLLXEuAEwEDrmUbevsLMd0rLJsvyBfwmSXERQcibBYNWK6Tkk+fKkYqhBLfBpgWMK0OJ2eWMY03tMbgvh1Bf5us+QUFLkEJFpfxpYtNyAetxJYSjnE403Ytfs+tLV9qrdPw2e4elR6KYLmDBlDUgogWyzU18tlo9h6HEnECCO524R6274apBbVImYuS0aITR5Jw2uvvYY1a9YAAK699lpIchi8kL7Y9vLOEO7dcwC/qOqeOAJGNuVYv2EB/0VVA8JKemuWFjPGcRxKSkos25SIMwG88Oe/xIhZJxzyer5qZMhYH8XUCy4+2peQQR8CL1sHP5kDsulgEEIBCrQ1W7WMNBV2jYytWH4ZeMUDJYWQCClxTwXlPoyYYVUMD7bbB15OZLXmqje3oqDfAJQMYnIIHj/7cI+cWYZL754KEOukhJhimyKRXGTDOvtXlLglPqymeiIAa1hcTysEWI/LygSZqyzJqW7KHpjGumJsgNnacPRFKxNqID3lgHOKcvHulOG2PprGVDx+0NK+p2omAMDjCaOtfYka2G99NhLdFBx3ii/6OiEaDQI0jnP6Xwu3miGcTT2o4hqxha/F854ltn1u/NMLtjaTj9zSTE2WV/+PRqGrqwuyLGPLli16e//+/dHWthgcZy3KbblO9Rlp74FlTCNjz48fjC3HG2oAC9vSE2+OZ88Ix3EYPXq03t5OQmh5YtMhz9mbkCFjfRRixjKWwREEL7MYHe2TLfMARylkwkMGj/UpRgy5oQTr150LoqqlKgoPAmKTWRFNbsqsHDYbj4Z6YHky1cOUkwpWvL4HH87djliIEaWBYwpRUpkDd67VxWHNLCZ64XL9WHLEYiVQFEHravQx1c78oOE/+LTplUNebktLG7g0MWOa69EpZiYdbvnfRizZ3XLojl8iNDIGjuD2wWWYlG0flA80sr9NagJEPH5oAc6OsLObDAAiKW7a7aEoHtp7oFdkmQLAUzf+AK888Osv7fgfPWMcW9ORlImCT13bsVqsctwn+J69qLd7KIvNC7y7H7E9RkFwsyvzsecfx6OPPmoJ3AeAtrYlkOUIQqH0VRLIIbTFzNgUZFa6HIFHsanMUrE7/VgmCOw54DjOcq6lIrum3vI89AQZMvY1QKqycgYZHC52lJyDDurXlMWgECZtkeREgAKby1i8hpCjwFcUQ6C9AuFwARQ1rV5T37dZxkTjE3TZPaxsSzyNe4F3jzPvqS91NEWw4YNa7Fpl1xzKLbYGgu9eu8Kybi5yDmhFjU31EfUK6cZHXTbFzHQkmtAUNbSY0qGtrV3NPDWOo+hevp7HjJlR1Rw6vB2OMJJauRmOINS5HJ+tucjWJxJR/zbk8Ieajra1abeFUiwtp6zZhcdqm3uN7EVX60HUbln/pR0/0FYFED8Ag4ylZjwDFH5/GwaBue8SDfbnhZpKBrU+bZQXS9QzIuyqzIGiPqiLFy+27BuNpXd/atDepJZE95ax9YEwXj/IyKBACDbXd2L+eGbtDnfzYvC8ov5rtbBr5J8mFdTftRQd850Jam9Chox9DXDZbx872peQwTGOg0IFJsWf1CmJpJZ/Y/WQqPEhoQBn8sVtW3s+9lRNB0AgQYGsqB9l4sNFt06yzGa92cwylpaMuSYYK8SYOb/80Jq0182LPHz5Q/V1TlX9vyTOYtMoJfgtvRM30T+ydUWyWHEUlay1Nx1A1WpG5LpzU8b7pxt0CFP7N40resxY2qN1j6M969ctYwRoPfBfhELb7X0S7WhsfN1SCifbP61Hxy/gOtJuC8adXZixXuC+fPqW+7/0c4RDOdDcuhoZ6yRW0eARI5dh0uR3IeYx0mQubaS5IVNLBmnQ3PnURG5XrlypL/t8Pr3CQjq0JSSEVGva1lC0277nrDfIUkcogQv+vhz/Xsjawt0kq2RlsXcylYxx6lvV/DcW6B9ebZ+o9TZkyNjXAKKn96bzZnBs4PwJFeAIMECbSROCjmzCyh5Rg2NQtVqlFhwVjeShsZFlctV2bkJciQAgELNOQsefHoLUYR9wK4bl2trYOU1ik1wOKobnOXY7/yaDtAkip8/sAehZZfnUrx0JQ7EHM9RAfqYab7KMqW7MLYsX4a1HHwLQPRkj32DHHSgX2bZ5acSiffRFyyEdbQ+M2U3JS616+8GmIYjFmBuypWUhtu+4HaGQIVOiF4qH3TJpRgVJH/T9UUvAsd2p2PRXjUDj6i/9HEmZg0gACgrCJ8HzSQQ4KzkqKakGAHDedvv+B9VSVSmifMmDVkInljq7k6+//nq4XcziVlg4x7HPmOVb8aNtdtfooZBUydeGavZtCB1CGcDna087MdETFABENh9dt/6hkCFjXwOIroybMoMvhqHFfuz73bl4rrEBZ4fC+LC2ATIhEIgEKBQJqNlXlIVcaUOsNtZeGp+FA0FmOXHn3QTeNRKJNSvR+dJLmHHhEIyZXaGf68TLRuCbP5+MM68ba7kGs7Ck4D0ek8+qdLxW0W30a6kNIhrY79gPAATBSqwUmrTEjGluSqLGuoU7OywxYxrKh49Qr5HtO0gpdjyfXGFknqVmTx4uuepJ9uWXiTeXsYH2ZjwMPmbEDbW0DIKiWC0V5uLO4bAxQBKS/h5mlq2F31Rovtgk69YcjOtaY+aBOJQ4ulmWyRR3XOdBK2n8dPFzaGk/dKWFQyIqYUrhKZAgY9r0+Rg/4f20Xalgj8HsfJvp86WSsYN/Xg8qU1ZNAkDuBYNt+5599tnw+/2QZfbbjBz5IF440IbFbemTSsoPIdA7K88gfdrr1xJkv2/YZJ3zeFj5M5433qN+/XegosL4fqRD+7zeXVYrQ8a+BhBdGctYBkcGRbKCh1va4KYUpQfeAOEoiNkyRollgNVcKALldf0f7bPDy3F0vPIKpp49CHOuHKnvw4scKoblgRcMUjTnyhEwx4kRIljizcwoHuC3rLuyr9KXO0xZfYNkO2Gi1Oqm1Cw3bnWQfe3BeyAlEhA91nR+j4+ds3HPbgBAqeJgtaOANCoXydFs22Mf7QGl1MT9Do9cHU2P3Gf7DWtLGbG6gCgImputg7gkGcH48fihM+sAQOQlzBltxPhRkyivuDOAGat2YHFbF0xhT+iMHN0s0/d+zSReCDhw4NDeaDxvG1a9jJLrf4eld/yfZZ99nfuwYN+CHh0/JsUgKRIQU5AtFuA/nk/hcsXg96d36bZFgESKxl2iugs0qUB2yFQOr26EHIjDNSAbTa3Ntu1ZWezZ19yUAu/DbbvqcPlmI3YycZgWyn5uQ0rDbDF2c0QvpwUA06e9jVEjf48Z0xfqbaWl++DzxRGPG5avYiXnsM7fG5AhY18D8BkylsERhkApZNLMMuMVijphgL6NgKJQ8WN6chioSsxYFUgZQtbpuvWIl2OQDjSCqgHx4RUrUH3ld/X1fscZukm+PLfFTQkw0uZ4bSlyGZxQjLLhcwAAn7W+q7eLDoWL9+79o2VdD+BXrS/tjQ3oagtDlq0Fyt0qGVv56jyU/mwKcmmWLZOMaGZD1Rrx2vp6tIYSqI0yy8XBHpKU3oA11QYZS9VPo5SgrnacpS0QMILxCwu+qy+3tnZf6F02Wdg43s4+t4WiiCsK+30UipZo+gzMrwJ7al4GAJxafiVOKvsOYmqs1I6qlfjzgt8AAHw1VvL6g+cuwItz78AH+96DE9qibfhw33uoC9TgijcvxqTnJyEmKShwWytAuN3WAP1I2HD3P+dhGm7b+DrUcIy0SJ3OVkQ5nIQSSYLzibYaqwAwYgSzAkuqZcxspdLPLac+E46n0pGgFINFEQWLm7C22iCWLkIsxE4Uc1BRcSm83n6YPPklAEBJyTlYvmI2li2fqQu/HoslADNk7GsAjj+6Newy6HvgwYRfCUctJhpKmevp+OA3MF6u1C1jvGYr4A2RSk4N5g8tYZpIB+68C9F16yC1sMHCXCrJl+dGaildjiO49s8n9uh6m6tZ/FFnohnRgYz8VPH2oF5ZjqC65gnT/aiBzOp9KJKMZDxpI4Yev2GNIypJPG/iqY7XQkwJCuG4hD0R5o5piB+emGw3wvdfOszWi9QyT6AcuktLIGSEvnygYVS359GkUQCA4+zWFgoWtC9u7YB7SRN+Xnt03JSUUiiKDKowy1yhpwIl3oEI7mEu8n3Vq3HGBpXQC7LJSgw88rSMX76s4K1n77Qdd0fbDsx5eQ5uXXoHznnjPHi21GDoAQqXZCdJEyelkDlVnZ6YSgatFHdjkWszAODgI6zShP+Efpbdgh/VQolI4LIENDZaRXp/9rOf6aW+ZDkMjvNgZ9j+3NrI2CHIUUJRkDwQRiQh47ZXDH0wAUAyza75edPAcV54PIaL8qqrWIktzwR7zCZxLGbfe9C7ry6DI4KMtEUGRxoCpUgIKiFQv7vPff96FsxvGoy1mDEeHKJyCBZXo/pv0/0PAIBOwuSAEWdz1QOzcNWDs5Bd4AFJkUcghMCdUtuS451JAO8yBEll7+G4UNT7gFZiRQGoDAIeruzvmLrZydiIkiHWI2mDiolFKZQyixkOP2bsMCScjjiK/Ib2k5NlrDusXWtYyRRqH4K2bjlFXy4raoPiZ7+xwMt45KRfmU+E1qSEcCIO/kAUJK6g8wgZFyml2L1zV48zVj/+97/w58svtLXHOoJQ4mE8UvM0puyhOFA2CyMP5GFzjeF+9apc5sZXk2gIsUnDOzv/h/pADX67+HacvUbBgBYKd4LinpcU/O4/Mvq12yfYLpeViGrhAj5fp62vBhkKtsdrUP7gNyztSiSJABfFG2+8YWnPyTHcf7W1T0NRYnih0Sr4DMDiWgTsDniZUqzvMuIB4wqFg+ETvEQhdeOP5zgRiikhxO1mfTdXbXM4WO+mO7376jL4Qrj47t9g6NQZGctYBkcMlyd+CQD4QeJO5CkyqAIQhYJri+OU8iugKfxw6oAsqIPte/XPQqYSQOzPotTYCDlkfJilNuPjnlPkRU6hFx6fydVOnEUgT//BaHz7F0w2wUzoAIB3jYQ790cAgITALFETJOcEAGcYAwIhMkB4EM6w8m1bGoIrqx/cPp9OxlKDozXSZTYaKZTiwyW16hl6MPALZiJ3GJd/BCErFB/uMGKhDoeMzZr5MVpU0j1RGgSq2J+Hjg7DUjOS7IBSzILJBV5CnrsLAypUaw0F3jzYgS6za1I+Mn+UNR+swLyXXsTaRSsP3RnAxveNcmDn9v+hvly9ahkmvDQT8QSQFLKwc+R3sXncj1H9wTwAQNJUWkvigLNeOwuX/Hc27l79AM5+4zzwm/fjmg8VPPK0jH88blggZU6wPS9a6S4NmiVxYCVTzY/CbsHaytfhgy2fYtMmq1o9TShIiFZmay43pFVWAAAPZ9CIp+vZb9uSsCa5NCckzDtgvNf/qG3GOeuq8Fknc60u6Qgi6vDY8HEZCZp+8kSICEqNc8lqIXrHWrm9QPakO2TIWB/G4IlTcNHt9xyWCnIGGXSHlcoYDIrNw2plFIoUGfGwarXY04Wbx0SgUA4EFH6wAfScyDickBypSkYAUOO0cn3WD31woeFikdvtqfgA4PGJcOVcA3fONQBgq2t53LQyFPbzI7z6M+yeMROhpUutByDsmiI+RvwKFHsx8XQwW0ioEmP3YZbaIFlIxhOIh8OQtULFyTSDCJeGUPVkrDCXUzpKg8vr6+vx8U4jsDu1sgB1sHZpcLuNUldTpCG66dTtYu1aRYTWVhaDWIg2jCZMjNTrUt25Pkai3YsbMSLehGDciJUaJO21nVNRZCz+z1PoaDrQwzsE2uoY2azbV4N4PH7I/i7OgwIXi+Hyi6YakfwAjKijyI4CSZFZT5NCFhL767GpZRNe3fCU3rdV5VK7ZcOSZfLSIsck1aVwPCIyu2+N/AYCJSgoqENWVgdKSvbC5bJqe60Qd9muO0IYeQmFQja/94raDfry9ddfjyuuuEJf1wq+9+9/lYWM/aqqAQqljuK7P9tVh/2qS/6hfYxQ/7G6CUFJhkyBVptoLRD4tBFdXend96mWsbbWTxz7ZU0ptbxsifogaC8jZxkylkEGGfQYBT4WL6LwLoiAScOCYnn/UgDsm766ZQHerX8KecjGSLkfZCoDxAfC+THrm0Nx0lhr9lfHK0ZJoQO33wHFYQCMhZPg+HwQjgUM55Wyfy+9eyouvn2K0W8rG7xDiz/BVfcZ7YTwEN1Z6GhkriAeHPbs6ZkAqc1qRXjAnABABBCODcLRUADgCLoWGRpL34xPh8Crg4pp0DMTqh4NDSZSmDxKavORhJV88bYC6GxYWb7sMpSVXmLZtmnTZn2ZgOi1S9s7NOLA7m/H9jlYv+5cAMCAQc1IDs/B4ApmQdTmlkSi2Lwyhq6IQcZqqF2Koau5GevffRNv/OG3Pb5HSdWS29y0C8889fQh+88p/y5O7/c9zCm7zNLuVmK4/78yfvNfGQkXI/+CHMOG4B7845ErsGj+43rf+iKC738oIytGcelSGSdvUnD3K/bfuP8770A8/gS0qbpiGoHlOBljxn6CKVPfwYiRK2yyIe3ErsCvFRGXZRnuwVbLWk2bofNWWlqKvDwjQ1gjYz7fcfhTtTX2MqZQJNK4d+/cXWeZ2CztCGGRJomRhhw11XdhyuT/YdLE52zbOOLSJTYAYO++P6KkpBg+n1Ufjc926eQrXtOF5r9vRPDTIyAxcgSRIWMZZJBBj/HRz04CR4Bld56K3d4CExnT/mWyry2xOgST7eDUOC+FSnDnfBeTTh+MyWdWwqcSk+zTTwMAxEyDNAA0/uqebq+j1DRwlFTmoHyokTkmB9nHvWPePBw440QMGGVYKiTJh+1LPgbAkgqiEWO/9nZnraJBcrGjC9FicSYCeNcwAEAyFgNx2xXBnezTEZMuVc/ImLEoHSGXXHcIO2R4Cqa4vOToPJubUpGZxVBRRAwadJve7veNwNq1G+AErValovD6PYbDBdi7ZypkQYQ8JBsuNavueGJYPKNBgtqgSezUYUCPRyOWf3uCSGs7+vXbjs39B2NjOgunCfku5rIu9TKr3UfiFiwUNyDOMwtQThTozNUqQRDwEsGtbyi4/TUF7fkjsXXUNZi0j8e5ayjm/lnGpcsorn/X+by+8jJAELHOVQ0A4NVi2TznLI7a2cmeS7MobOrz3NnZicKrRiP3HDuZTUUotBsbN/2fek6vbfuZa3chof4OZxXl4JbKUn1bXKE2Nf48gb0rFWmy/ikhyMubioKC423bCCeiufldS1tZWR5EMeVYHPRnQw6wiV6y/uiWE0tFhoxlkEEGPUa+z4V9vzsXpTke7D+5H/IoIz5Es5ZQFhsVkVg7r7nyXGNBOB/6i40ILV2my1fkX3ml43m63n7b1mYWeRVcHKTWVlsfJR5H2z//pa/TRAKnfM+UsUeYZa+qax3ikMBxBtlIJKwDSzTK3EqlSp49ut4WxyLox07EIuBMBdA9VATnFkEc3DDPLqs2DtkDbkUpIA1kxKW7wOYjgRV7WzHm3vexYq/17yyY3axFbls2pSwb7lvR5LIrLjlbr4bQX2YSBMFgEfbvm4Tdu47H/v2TsGnjWZaYuqTkxglgsgxDA8zSGO4wYgaVXBFroqbzOxDUWFh156VYEufedgOevOEax3snpRuwdugIrBg6AW9NnO3Ypzvs55tRz7eDcFlQ1Hdg35ALQZUQQlklOK7eeD42TvgpmkunYuuYHzoeq/C665AoMFzqJCsLSiKJNj4El8uwCnG8nTiH4YMg2P8mAcKIWWkpI0qbNm1CQ0sjPKMKDnlv6zdcoZe+cpK1qIrEmdwIgN8M6wevyY05ITsLQkrYzO9Vl+UFRcbE6KwxZTh+GCO4WyJR1MWcXZUcZydwogtIJpNwm6RxCEdYcpFC2TKOfgWLVGTIWAYZZPC5QLO8yFfjW0jMGOgIKNxCEdaPMqxHxMUIUet996DuuuvQ/PDDAAD30KFwgnfyZFvbqFmGrhI5UIOqE2Yj2WR1kYRX2gOuO++7C1NUIkeYcxVVXRuQIElLBprHY50pr13zTXaf6n8WpGqIERFErUIQamuD3MFm31fGZuPb8W/AOyQXk6FlERrHiplqAx4iCZEJxAKAyEEQuC/dTanpPT3ywW5Le0WeQVopIZaYsW1bT0YyadpOKbzegQCAcCiKpF5KSq1UIJegvn4skkkP6uvGIhIxBlAAoAqPwdiHF+glyE8wgl/VaWSpcoEkasOmZ8+hZmXngU5MLzoHYsIqBtxWX4tgm3OJnAVFw/EmMVyszdX7us2sXM/vw9Oej2ztPJ+LjeNvAAAocgfigSeRjLyPYa2D2P2Zr6dwjOOxS277GZI/ZJOWcFYZQh1xSGqhdHNcWHGRNbFlGU7ED8lzaBRLkQr/t4ei9NbJ8JskWZ555hmIxYxcBYlx3NNOO82yb37+LH1ZdDmTt6T6t3JznCUUbUlH0JYF3KLei1vd8MSVk/HPq6bg75ezbwCRKH63zyqxoYEQBzImMDJWdM0YFP9wHEp+MhHQrLkKNd7dXsbGMmQsgwwy+FwQNhbDyQAAIABJREFUCWf9sEYl3RWg5HRi8+AatMRY3ElxyxZUHFgGT8xqZeELjI95/3/8HUPeexdEFJGoqUH9rbfi4MN/hBwMIvjJJxBN1qayT/4JAEjWWeM+6n98ve06g++/jwN7GGmklJEkWUkgi7otmX95eUaGYEPSsJj0UwpAbJ/KVOYkABwb2NoP1OutXrjgggACglHYjjzaDrnUICsJ2Uxiu4c2dlAASVBUHaL48heFWy0Wva7GGt9nMcgRazZle3t/DJVLMVxmxLmhoUFnHKtWrUWbminLq3dbzXdfL1CLhwKgZ17+ePy/LX32dhp9XBvaLbVIAaBp43YMzh6HE4rO6/ZcZkgpOnIvPPUiHr3sfPz37lsBANuXLsbKV1/Ut68XmZ4YBbUU7OaQRGc+01WjMnv2leR+tBYyUVzqkF3sBPeQ6QCA1dPvwXO/WIFYA7MUTZr8HhbgfMzDVZAVa9mvJ8jNAICOHLvrsQMhiKU+SJKzFsgnIpOGGDVqFKZMGYhg0Ch35XIZWcTrY85kLK4+JCIh4EwfiZ3hmMV4eVyWB2cUspCD/qp+2YQBLDbNq4k3yxSewxDVE4QQJEli0jdD8uDqn21YwxSqv2ixHc6JQkcLGTKWQQYZfC4IIJiUbWSveZYcBJEoOFB4y3JwXqeEJU3z8W790xhQvwwjd78ILsW9t751o76cfeqpcA8ejKxp0yC3tSH43kK0P/ssaq++BvU/vh6k0yR5EWTB3ErUmZAMnv86+v3lzwAA34mzcea1rM4lldkMOyIHUakUp838++MSpks2MzkchTTbxpSyC6xWiEHjy8HxeRA9fnQetIvJcopqIQQFzTFKvyytMsjpoZKeZY2NEWYtWLLRfp4jgbr2CAbdtQCLth903K6Y2Ri1B/AXKH7Uc+y32rJlC6Ix9lslJeNvdnxyJHoChRpkhQJYtvQKVHitBC4iWwnNqneXGNsCnajZzKylnIn41G7dDIG4IBIXeoKDXmBI9gQc3FeFl37zN7z390ew4pUXbP1ed32GV92r9HUOzBKoEHMlgTJkRZuxeuovsHH8T/T2XGJkUXrGjwcAlP3pT1i3sBoDJkzCOxfdrG8XTZp788jVWEAuSnvtMqgto/7NN98EAJOl0hnBYBArVp6Mz9Y4E9mDst+xfW2AEVI3Z5/GaPFkfp7DnkgM/1ElLzQSrcUkujRdMIVaMjbNMGsPFhefwdq4x6EoCmRzgXHOZBk7mmrJ3SBDxjLIIIPPhemkH2bsKUVRaSeoyWpFQFGcU4xrAgQSjSGYbIM7aSdNr5xAcPXCq/HtuwUM2roerdFWLKxeCM5v/cDHtrFZOgkbgxWfy+JLwisMt6QcVPWmRBGeUaOQc9ZZIFlZCC9ZisT7b+KHv00pPA6CjmarMKsGSRH0PgAguCZC8Bpq/y6P1XLiU113yVgIWxd/YDueltiWGuxu7eQ8SEQSElbtazMKg5v6Ha68xZ7mEFbta8PWhgD+vGg3pj6wCPNW11r6vLWJSUCsrXGud6hdh6fCC3h42z01cB3gVZJrGRBNyIKzVlwqRsmGa5rjFFDKgyatBIqkxIl1NRnXveCxh/W4Re23rN60Hq/c/wtcMuhWXDzoVsQj9sB+kuKWnnv8uRjoZ89Pw3ZrUW7FZN3s4Kyubo4mQClF5UefAroeFgdh+EiE/f3QmX+c3rdo4jB9ufinP8GonTsQqJyBVW/swwt3rsCMCScbxwWFh/aszJ0Ub0B2NiP9hMhMJ0/blmIZe/HFF9XrZn8r59/PeP44zngPLi41XMxvNLN31cXZIyV3qIXiQ7Ji2aY9ywKnZYcSUMJ0DN1pCRTrO6D/1fD7tMoOIfu9mclYL5O00JAhYxlkkMHnQrHiQWNLFJzCW+IvCAEK+5VjXv6tgBpP9MxpVnXwVSeW45XZBoHriHXg5JdPxu2f3g7uzhuQNWOG7XztzzwLEGDgmEJAzZbqeInVp2u85x7snsZcOf0f+6teboaqA23Tvfei7sc/hstnJWRmu0Bz8yB9eTjHXBjaAE44LwTPVAjeOQAA0e3FN2+bpPf35XZvYSHq4Kaon9zkcT0vZHz7q5tx2ZOr8PEOe9HmnsSNNXRGcd9b2/DL+Vtw2qOf4rInV+G8vy3DXz+qQmsogV/M36L3jSZk/PF9qx7VyDKrHtsnu5hlKlDJSHPqcFtEs8Gr92nW6Go+aCe+pybG2toGoRSXxGfiW/GZEHmDDGQrLJ6pev8kS39zeSm5wouuToOMte2pRZFbE5GloJTiQFW9Zf+//9/ltmtwSrbY7TGsmCWegaj0sxivaDAKt4N4LQBIoohk+B00NcqglJEQqrTDd8HFtr7URHKy1JhJ3qQav+VTQ2oiVbYCANpQaFnvR5kL34MoJkxkGYfHn/AqJk40imynWsZ27dqFMOJIqISNTxEM37rtFrS3LzOuw3TNV1dYzw8wN2UyxW08t8GeeAMYCSnmbF2fyAMKTcufNIuf1zsAPG9NwDETSd1NKVNbIkdvQaZOTgYZZPC50JA7GQXSWyBkLMxjFwFQVjkaN5x9MuZt3gy5az/qR8Tx/eMEgABRNwFgdTWd+dqZ+vI2qRan/2cugosXo/76G/T2rgUL8KPNfwDhCar+zUgWjcWQqKtD5yuv6v2aB+Xhoucm4MnTn4ShjATEt+9A0RV3oqV6KJLhN1Ed2gZVmxYAsHvX8SgpqQYATBYb9HsBmEYZAPDuCQBklA05AQUVhgXPvAwACS4Gl2IcPP7/7J13nB1l2f6/z8xpe7a37Cabsuk9oaQHCKFDAAVUqsArRUXFhi+gIk0RC8qLYkVFQREFUaRJ7xAIhATSe9vsbra3U2ee3x/PnDMzZ84mIQlk+TmXH8w508/M7DzXXPd9X/faDqi3yZjcA3lzYmWDSlz//J/f9sy7b/FWbnxkJWceWsc3ThrPxl29/N8z6+iKpZg3uorfv7LJs44TNbTRRglLNrcxo76C7rg3bGXmJDrf8/oW1/fMOcpUnw42y7NhyjVr1rB+/dlMnDgO2AxA0NGeLSK952FhZCp6XO2zJV6eLQ/QTJ2PJ2bydtsmdAwMy+ctsMmhRhmS5TVpPmV9Par6U5QEbMWmc1cHXS05Spj0qj9lpV7iGwwUUlswksbYJhYOtglcd3sXYRkkkdujE9CFhplaQ29HgnRMVYVKs5OO5q7sMqnYqxjx10nGrqX+wQcw2trRMj5ZeQShQ08YTueSjRi4c55u5Hvcweey3zPqnuFsQSaSFBWr9fr6+vI61e+Yb1K8roTWrm5OPvlkVq/5PgBbt/2BpiZ3lbPTHX9iUQFRXXMZvqZNyZMvbIFBAcLRAAlT0p7Kr5a+sFY9E4KOkGQ4oBFBkOgn2T6TwC9EgKFDP8X6DT+0vhuu3EFhkVppSrvitp/WaQcLvjLmw4ePfcKoQ45CdC1VD33Hq6sAhk6axaDiCFfc8UPmXHkd5/aOJRYRFhHbPb72/Nd4YvMTRMaP98zTAwKzpSWreAFsOP4Ee9/BIMvSioBc/pTXKqCrJZZtyVRvKRvLl53A2jVz8+aPZZWxzL9CJxCZSc9992Ju2UCw6BMEoydRUhXhsBNt6413mp5zbUfDrYzlq5zMV6338roWNrX0uqYFNtrtf258RFkM/GPpDuZ+/1nOv2sxb2xqY3Vjd14itkh7nVcqbubt8OVsjpzH4sgXWRe5kD++toVr/7HcpZJlsLaph4U/fs57fGn7+9q1c1i27MTsbx1i2ondhhGirdNedkT10OxnPc8QZLbbKmqwcySNjariVkidKlnCcalp/Iwwhw5e7llXb4rTU9TLxv+8xcr7XqAkUE6CFHdFnmFdsJme1m5Wvfyqa53q+iM828kg/EIjgbWqtVYagwW1n/Is07G5Ea2fobQopBpWr3hph2t6u9WAW0qJEVc5Zutf+wG//1kTXbWTs/O25UkynzR/CJWDo5g56l2rqHZ9z9xrW6jPe2wPPfQQvb29nulacQhZHmDEiBHU1dmtqdat+65n2aqgInrfGjWY4oDOUzPGuea/sr6FlataCK5oZ1qRUjYzNhW/muRuR5bJn9QdIcmgrqFJPOrazkSSb6/bjtCVaiuEbtlsqN88esyb7kKODPFKm8jMffsh+PS9H/hkzIcPH/uEaUPLSI+r8ZAxkESK1GAcKihg/vzZnHbZX/hym8ojmewIXT22TeUn1aXS/GvW97LTb118K8EhQ6j72R0MvuUWtKh6kO/66e2sX7Cg32PqKwxw/avX9zs/nTSRpjuvp7OzhqamMXmXbxXd1i9ysycpAmw58wz04HD08CQCIZ2oS+1yP+gzZMzAHfYZV2MrahvXtLGtza3aXPC7xZ5jys2ROlV7jbnaCorpY5Ro4FuBe/mM/jizxCr+GbqOjZEL2Bw5j82R87gzdAd1fauoyHFjf27Zeu57YxtP5wmFAmxq6WPu95+ly6mcWackFiumqXEMqWTUmiyYlXZblqQcx5yy+hbWXjUjS2LCun3uNEfSvo6WNYQVhsoz0xBMI8pJo20rCelQOQQaf3rt3/xtzXPESbHDCjmvCO6gp6MbM7XRdWyxTvuc3/WlS/j15y+iA6WmibiRVd6cxLFJdLJJU+dqy9tvUjtyCUcedY/nvI0qmQ5Ae6P7uu5Y+R/M1LZsQYmCIg8blu5i8cMb+d3XX2Lpk+58PoBQgUaipw8pDBqx20vNlq+QIoCRCYVbNi4PWxYdZWXudlDr1q0DoLraTeJeeOEF+vr6KCgoIJ7ov0hk/vxXsp+PtnzQchPts5WUJrzX4z4HJQFHUUOznVMa1N1kTEh4o7OXFT0xfrRJna9vrt3BXdtbeMdQf7ciWyChzmE02uFWxgKOMKVj+t42gv8w4Icpffjwsc9YO2swWrPEmcJionuS0YuKiqmMz+Sz7UuYnhjPFbXqIV9lGLy7yRpw7v8094eCnF03mNZ4K429jdQefzwAhfPns37BAlp/a/fyG/bb37Ltsstc+7nltCQZljAyVAaot+0/Hqtx0TMmmpFED00g3fckO/s2ucKUGTjtLnZqKv+oNRVHd0XU3G/qW046joLb7iZUcjHJrrvpSrkVDYFg65apmCOswco6P4YpkQGBsN7W//rmVg4fUc4xE7zeUBkkp5cTWqaOawgtfD94F8Vi/2wu5mkreNLcfWuoxq44026wixNkuSJH69bOwZXULfEoRbsabFKR3qWO9Z0XHyeEyvMJpjUSQuXW6Y6kcIFA1xV5Mww7YT1tpmhtspUVoZFJT8RI2sdyb8SurDSRbF+l8qiiejGPhN4ihUG6p4eW7T1UDonS2awqSJ8SJ3t8qCJSHVdRoJx/h5Vn3BHyTFLdfVQf+lZ2L6ARDMYBiZEwEYE6cqHpg0j2/N0zHWD5s9vzTgflVfbkr39EfH0XZYe0sQmb9BYQ42JxP1PkMr7ET4jhNmStG7oqd3MUFbcwYeI9fPJTD/CLO1WFpZSSWCxGNBqlteU5zzoZRMK1pKR6wVq6oQ1RnWLIIHcbooxBsJCSm8bW8Y019m9z/gWFltp/L87Kz6Au6EsZrOtLcOybKpfxyhE1Wd8/QxRYx+ztj+okWtkwpSFdiljf280UHt7/39qHCV8Z8+HDxz5jRvEUT1pL2sj/WKk67lsc3VZO35zrObpXvSVHcga8SckUM2IqTHX8A8cz9Y9T6Uv1EawZRGDQINeyqxNbs/YVAKseuok1Q9XRPL11Bw+vWc5lV+p84fM6Gwar6TPfupVBLSoUt7F7mecYF79+FunUD70HvwffCd1I0nHLd9B0pQi2JnZgOsZCDYFp6oqoOtCX02rnzuc28Jm7l+y2SlJGbbLSQBWfT31lt8eGFoBDLrC/X70FTv2pml5ejykFvwn9lM2R87gxcHfeTTwduooA+T2pzJzwrtfMIOdwrDvmpfvvps9SKUMW0Qnn6AMrut6gt0ed03RXLY9vv4v/7Pg9D275CckOu9JSOkJbCaGT0nQSurvaUCJZ/dI9VIaHcNrwK2jUOmjVuiG9gdceWkmsu5viYAVHDDoT0Z4g8qRDSYqlSdS9RoIUi4bZ4e+lT64g1mvnf2VaE82Z+3fmzH2AVtGITO/wKjB5LDW0YP+tiK74haqkTHb9gQ1LFpMMBxg1agkF2GpTwqpQfU9M57Pij/QId+FFRYVTGVP3XWWlIqc9PS+5lu3r6yMa7WD1mm/3e0wAaet3feevyzj1Zy9T6Cg4qFrazp+tSl2tPZkNaWawN95hQV3zkOKetEnIUuDSedoxAQSDifxhSsMRpgRSzXvfIuuDhk/GfPjwsc8YWjI0T2VX/ofsETMOo/DKVzlxwRHc3NLGs1u38445hp+kPkF9/C8sSPwEgDub3Mn9Zz9yNhc/cTHpZncI7cp1t9B9xFSG/e4uorfdzB/eVqrZm5u3UWMYdMoonYWCXWWCwRVWY+O+Jmqa30IPTcaQaRYm3a7nyWSURsfgmvktQ7c/z6SVd9tTcwaIQDpGUaNSHqYe9w0AYrYTBgKBlIIQCdcp6kql8/oeXfsPbz5UFjmJx6/LKXDcjerL5c/DtTvUf9WWl9d3WuHjd8INnXBDJ0a4mB/JVj4395NMLTN5J2ITgx5LqfpK4AHXPv5mHM36yIVcEHrBczgyp5IwQ7aKzTyyIzAvrXIBTUy0pDofh6TrOSI1gdOSM9RxpDroTrVREEvQ3DySN9/4GC3NUbpSrXQk1f0xOz4su02RMDltlAotpjSN++cfzR+OWOTar0BQVjaKstBw1/TCQBkNS/9G+85WThl6GXWFY9Fb3Y3qIy82ESvZzINhd9j4ud9/k6Qj/DZ12lOMHWvbrSRjKj/KTOeoXTKfv1f+oo5PXD0DoQkOOc4OJ2qmoKCgh43Y4fVEP3Yhc+XLnmmFhUrRMtJqn+l0t2u+aZqEw/1XHQqLTP5si9uLLuwIU/Y09/Hou3YYNqhpLCi3CeL8MjtEP2Oku/NC9jikRG+Kg6OzwklvrSVkvRwVlc6lvHwe1dXHu9br6y3l6aefto/XqYw5SFqoLr9P2sGAT8Z8+PCxzwjUTPD4TGn9GjQKRlapMEaZaVJtmHwieT13GGey7DsnsEXWMiV+F1Ep+T8HIdvctZm3mt7CHGkPvusHQ3dUsKFjA8vq4dSWG9mc3snUeIL7U8fx5eQVzJO2U/ui8d/gy5cr0lAQa0GPzCSiR0kJb2XXk1vsUNwgU1lQBNIpapvfZOw6FVpqKHcP1gKJbqoBdu0bKoR435J17g1Lje/wbfSeRJaM9fbmN93825LtnvwxezPCZY2RloJbgn0s/uyTTH3qQqb+dS7nP/1ZfjHnPKaOHM7UP05l2h+n0Zfq48dv/phD7jmEP638E680qJyfi4bYYZqYDKFhUojbiuRxU9mGTDbdrZHAHdYFaI5vZ1nb8xyWzu/hVixtNWNIeASXxo9llFnDBKOOUqnkxEe3/5rHtv8WjBQzUmOIx0sQOWphgelWviotC46E0OnR1OeuCrdpLEnN05B9RuUJxBJxmjY30S568rY1AugNRegTiZypJqHGLhJxdV8XF7dSO3h9dm4kaA32Up3PKQsVaZDSTX4cR+iBaezESKeZfKQjt8v6G3tQnAMoA9U4bpVIdCSI/GcHSXMouRCa+puNFKgXj5aWZ1zJ+gCavt6zXgazZv4TgFW98fxthXKmSSCqacwstcOYQgiWz5vMj8cPY1iZuu6/u2iGa70Nu1SBQXBNZ3batniSLY3dhF5qJCUrOezQewhZhRLBoLLXiCeKWLVKvRxt376djj71O3f9cplLGQuU539hOBjwyZgPHz72GVXDxnkMMvdoJQ/8IHUOTxmH8cmZ9Tz8xfmURoNs+v4pPPCVEzk18V2O6Yvx7RZ33tVlp9thlnsXqkfXU1ue4nNP2+X88xODaDziu5x9yddZcdNJ2enTJh3PzkrBFz+n89vjdgAaQmho/TjwZzDdqFc/ycpJqWt4iVEbH6ZLf5anDxGEkl3elaxy+7c3uJW8cDhGHTv4RPJxXOphPxHJI3/YT76OLjDq3W/0962+j0ufvDT7fXnLcn753l2OXUhm/2U2f1z5x7ybXGP5tqVmfo6gMHl4uNv/64wFs2HEfNJ4/bTMHGUsnurClCY1stSz7GHxOQDs7NvomZdBzLBJaFqmSQkVHrXVyCDhsq+yoeVN13p3v6pCYttj9oD/l6mn2QsIaOnxHn9PugOJ5OW/LfcoX048Hl6Ud3q6+hBeF3P5Hjd45oUDGTKmfsPgMVZrJNNbxZibhwhgphv4y7e+zu3nf5x//+T7/R5bRTBAV9BdNBHYpvbR1+XNWcv8zQ62iGMstoWPfewQZs2alV0mHr/Psx7A5Mm3U1RkVzrrW+3fstmq/K0NuEOSBWGduWWFfLW+hscOG8u2BaqwYVA4yAVDKkmmTUZVF3LsxH7yt3KI+IqlTWh9Busa3H9/s2aqvDch1Lns6urirrvu4lf/tF/MnD5jAymB3ydjPnz42GdUFoXJ1RqcLUr6w9izruPdI3/FrWdNY9rQMms9wYTaEq677DweMI7i7O4evt7aTr3lS9QdFdx0rsZlX9JZaSXC/3P9P7PbvGlXK0fMuI6rT5rAvNHqTfn2pl1c19JGbY3Kx2kuF8yacTRHLCynK9kKecwzTxl5SvazLjXWdL6JZj20NWlQv/U/mCLNfQs05iy+kSNeuZpfLHL8ZsvxfSjuEE60SHlvtRYW7bkRJVBMT97pVXLtbgnvWWPPcn2vK3IPxnceeydfOvRL7nWGjODwsq/zRstGQuEIq3a5r+GKpi74n8eQsz7rmv4V+UOvJUg6TmV4CCUySmHUrfwNt8hcJgH71eZ/eY7/+SbblDSkhUlbmflBqREquZhQyacRQiDj+dQl2KQPyztdgkWK3Nc8YcSQshdd7j5/KO6o9qitXcvIkW9REKhjZEEZv4l8npViaraSMYOt2i5r3+o8BMJh9GCQmnpvSLK4wjtNmrZC2bzZbj1GjvrclTbYnnYn7GcqgPP0Tqeqylul+e575zB5cv5m5RkcveBdamtsgruouhS9yS4eOfrHz7Ny/mQenuYmhiEhEEKgC8FhpYUEc0LzibRptz/aC2QakcfSbgIbiQxGiKJs6kRGHXNhgFlaZOCTMR8+fOwXRD9hyd3hzMOG8rUTvD5iALNHVXJ4qRpoL+7q5t/bd/DyFpVo/F69RmeRl4gMTaUY11XF9HknuqYneqYzvbMMoWl8u6WNT3d2cdGiHzLy2Fm0JLZTado5LGPTgymJFlMddeTmIOhNd9JTrLPu39+n6kuKxJxRczjHlY4gYMQJpXpYNlKwsxwisRZUkbrgE9i5Q09s/x3SanodJLlXZOynwV/lnT4vuMJlVKoXruah0x/ikimXsOzCZdww7wbeOP8NrppxFRdOupAnznqCt85fyi1z7+CB0x7gqKFHcfm0y3nsjMd49IxHAUi2HUFr4+EsXV9IT6oDcsK3z6xq5ayHz6K9yG2DMIr1rgT+E5PTGVkwgWhAndfxiRF0B23SVGnlNTX0KUUmbngJZ7cjf6nLDDE9Xc8oo4baeBhNr0DTyxiz/gHM0DwunvwXAFfP07TmDl+Gw2ofAtDMdnIVKE1oqol3wu4pmW+4HpRWxGqZvoWx4xYzdNhKBkXK2NJjK3S5FYzbS5QPXFGZpEAvpuTRAKOLDyHR61VUO5tWYqabkVJy+MkjGH1YNQsvmOpZ7uzrb6Vu4hSSSYscxtJ0duaGTyHQoMilIi7uG27osJXccMMNlJfNcU0vLHRXQ2ZQVXUcdXXnWV5eNqRUyflOhKRA5Ih8XfE0G3blf7kASBpmtjF9XnjSUtXviedx05eyh2hU5cQ1NtrWHG2WnYt0krEBxMt8MubDh4/9Qmh3D9F9xJXaN3nZsN/SS03J+IT7oX/XziamxhPMjsV5dPtOJt/kTXqfe/W/KbtK2Q5Mnvc7Tpv3B0IFhYQL1YBdKW0yFhNJuvq6ee01m0RpCAQaI076OKeP/TiVn/kfKi+9hNE3/Ipvn/1QdrnOQvjL0Roz37pVleaLMEvbqrLzTUwCVi/BYDi8V2Ts0tRVeafrwkRgoJWowXZ27XzGlI/hK4d/Bc1SJQsCBVw0+SK+MVMVE/z4yXV86fd91BbYeVzDSoYxvEQlswvdETYTBiLgHTjXtq/lF8t+6ZqmYWRJJsAws4qGvvVZ5as6WUqVlU81MzU6a567oVs1iDdMr2wjpF21GdPriRLmmNQUAqKCQc1LmLTyboZvf47ynV0M61G5c0EjzY2vWWHZHNVw1mx1nYplAZrRSFmojBX6Ns9+NRGkKxzhzaOGeOYB2crFN4N2LtWc6lORjpeRWE7elpQ6R9ScRUfDM9RFVbL9oaXH0NaQ374i2X0vRvJdIoVBTrp8KiVV3qT8wooKSgYNRtPUuYu82ET45fxN3QGSSMv7A2prz3DNE8Idtq2szLQ0cpOc6dN+zYTxN7umNcSTPNbSSS5Ouv1FuuPeyttjb7OLP1Y0dFJ/zaO8u12t/8amVlU5mYN3vmPl2IV1Au+2E35+p8UA1TXuS+av8C0vVyRs6dKl2Wn/sELQmTClXhEhODg/+TwY8MmYDx8+9guBnP51e0M09oSLF0zigtS3qI//hYWJ21hijuPqtnbO7urm9zubeGPzNmbHE/xlZxN3NTaz/HRvc26A8sIQNSVKQZgy9yQmzjgGgIIib0hou97qmaahYUoDPaRCj1pBAYOuugqtsJCQHiJ0123U3PZ97mpqZmOtIJiOMWfxDQhhh7RMaSKlaRvWyw5cJ+l9nC9jUASBSVQP8elPzQPg1Q3e487FE++pwam919v+5tpZ17rImK5JPjXTthEZXOpMcrY6CRQGst9yw5QtiR1kJIdhqSEk9Iwi6LW1NHPsMkxpYpqZ3oUBEEFWdSjFKiV1pqz8A7XNSomasOp+Iu8p9/x0MMh2/vvaAAAgAElEQVTcv/1JrZbOXwWYxkTXggTK6ngtaBciZMJ5uhZk6eyhvCVm5YteEyi0w3EN1LGG8SRJI4WGZimVPRS5QpWDzOIsCeszlOK3u3w5AGm0EQyrv6mGdd4wWzhaSNowkEIiurzXMwOzTN3jLYk0N8kbAHgjNZJN2BYahuku1Ni2/W4ARtTbti+BgDf3D+DxPEQMYHt7jNZer1LnxC+fVyHX037+Mq+sbyGeMvM2pi+LhqguDqO1xAk09CESJvqmnixzeaa5i8ZE/iKY/pBq6EUrCjL4f2eihfL3FD0Y8MmYDx8+9gseZ4a98A/aE846fCgbbzmFzbcu4rqLTuPL0R/wbvV3OKGtjklf2kTzF3ewwVQ+UzelPs2EqTP2sMX+8anEPE5P5F8/bSbZ2P0OweL8jb1HH3EKFYs+zsxrmvnVhf8AIJDuQ5oqTPLItl/x8NY7MbHJmMj+3z5AE2iY6MJurAzs1pcM7ObL6TzLnTfxPH684Lbs9xGldXxv4dcAkNURjps2GCFg+YXLOWLIkQAkD1cKSpAUpukeRqQ0aYm73d5BKY+5yORPt6cVAYsbihSGy75IuOxz1O14gbiV0B+P2wURL0wRLB6XYMRrv1a/Xxqc8bBKsA8tbyf0ajOR/+wgYFlIVA/aiNRjhDVvBW08YOUD6iFWCVW44Gw5lYEZJBv++oa4g5vELWzRdtFcGkS38tq+LX7M5dhFEiHHqdFF/x7rR13wGfucmF0UFMPLf72HV//2Z8+y4WgUw0wjdBA9DjKbm4xuXevgig7WiEkAXNs2n2+LH6vfnWjEzCFjquWRpKpK9R+trDiKBUd5e6KCylPrD/FUfkLcm1DH+8hy2/Li3R35SV0Gu7oTaDF7X8F1Xeg7LWKcNnmry10MoWvj6etze6w5kdzSlbW6GEjwHfh9+PCxX8jlXoF8ssK+bNfa8DETajjmmhrgGOCLABQWwg2HP8A/39nB4huPIxzYtzfcjmQzZaFBlJDfPHJ1+2uYmISG1Oad78S48nEsLQwS6rMVlN60GmgKRJFbQXqfZKy+Msrm1j6M2gI0JAFM0lIS0ARpU/L3Jds4Z9bwftfPOKGnzfyDpJPMZewELvvMIfxsWzNr2uNIqZaZWTuXZ1gNQY0vB96iMNXL8YlD+U/wPcanVXhPYvJu+4tMLJsNwGijhg16E5PTKrF+k1AhwlDJpzESSuVq7FnPmtTr7IqreQXxTnQjyaCuHt7sWkJPqo14RydXXaLTWgy9Ber3VLV3QCOEax4HzSZ7WrciYWarQawywoQJr9BRvZUJnV+mCbVcWdlOEJItRjE0g6btfjhMyDCHz/grL7346ey0tDBACHQMMvpMXERJywASkJqt2mTImMyTqDRk3MTsZ2l28tD3P+tZJrudQBAjsFaFRAP2jaRv6cGot0mISPbvEwaQTnVhGF4Fq6pqS7bbQSqdp1rYQqVl4moW6Ohxw8UFk/2ok5+79y2uP81dJHDr46sBmDe6Mt8qu0VwbRdXLdvMouMOyU4TohLwvgwUCEfIN3AA5PsDjIFHD3348PGRQu5DZFphPO9yBxo3fGwK71x/4j4TMaEPZk2nnXxdZfb/Np3PdiAfpr/6JqP/9ZB3RsDtuZU7HKcmlmbL8fOhojDE8ptOxKwpQMOkzdD4Y0NrVulq7laDqtHTS7rdG+7RM47lhkRKSc8rryANW21I51SYLXprLRuTSdAEr1jKQ8qQpDMJ05pgWEopVWEzwtnxecxPK5NZU5pIx/lamJrCpfFjiVi9Ei2LK4SI0JNYzWPb7+Ld9hfZ0rOCPmvwn7jiRwza9hN+ccJaJJKG2Aaaa0w6Kk2u627l7U1beXfTVp7r2MLmyHms7ryPr3Z486ZCb7VyqVDqUkG0ndJQFb0pRZCnTnuaqVOfoVKWMKF0NpoWpFj2r9LETG/+1ivBNZQnNErpcE3/Mr/iEv5Mc8C+FpmihiHR0WholA+x/b/CBfbLgDTcpscAJ3z2Std3U6b4DVe4pgXXuImTDKtrbpSrcGUix1R29ZrrSCR2IoS74KEg2pXNR5Myf04WgG7l5mkxg5GV7tyrp1aqsHh51L3tw4aXE0/lV9S+cty4vNP3hKpek3sbWvnCSqXmlZRUZjshuOB8FzoA6v2Bhk/GfPjwsV/IdVk4ctRH47Ey6vBjsgnlAKckD8uzlGIOZp6qrXzQwmEi48ahae7WTaZMk0qpwXwhT7lOmoZEDiugqLh/RfHdhi7u36bIhtPXbYJldNp++09p/slPWTtjBuvmziO+ciWppmZWTZjIqgkT0eMq1JdIm6yeOIltl1zK6slTWDVhIomNGz1hzre6+nh0l0VMrGNNGqbd8FuATPRhmhoagmIKss77Upro4Rn0pPITm2gi89uDCK2c7lSrSy0KlVxE+Ylt/PLcGMaQFNXlswgWHsmIRRfxtU2j+HvvNUyN/4Efpz7JeYP+yZmJGxDApd1tefeXhZCkzIRHmSqWBZSFBiG0IKYJoiN/HtYLyWOtNd33wtDCiapC1oEOUY4hAmjCpNvqUzq13G7JoIsA1WXD+PR3bufin/ySQCC/+34GU485gfO+dxsf+8Z1AEgjwNtilutQzJIgoieFvr4LkibZuLiVF/UXLnJts7NzCYbR66mQFEAoqF6oNC3EM61d/HWnNy8xZpporWq5jS29/N85tjr1z3eUMvXYl4/k2pMn2NsW7oKfujKbhM6sz+/Cvyd0rGjlqjXbeLCpncZEimhhGYWFQc9yrvZIA4+L+WFKHz587B80x9h2/vwWPjn//IN3MO8DtSMLeWPJWmahfMVCeR6HGVNII9W/QpAPWngSZszOcZKyj8wIUM0uz2BgCp3urv4VvlhNhOu2KsXEScaunRrhosZu6np20fob2yR205lur7H0hvVQUU/3pi1cuOhmZjau4uq3lC3ExlMWkf7jf3bzY9Q/d71kkTYBCEGqeRtyiHARWgCC44mKLlZ0vMLs6lM8m0tZeUrHDF7D88l5xGKPuuaf9b/HMWTsRu78zhjWyGEc98vr7ObRpx/LWaiQ6bOr5/P1iYPY1T2XCbeM4KHQ9ZSWx+hszx9ylkilhJZWuKYnLVPZQ+edSmIdhLd4lSkAfWM3nVPKGDN2MXAmAIFAAjOdIk3+tjq6niKoeRW14mAlh8aOInmPnTsVEEHSedoknXvzjwDbMFb9FrWciNsKkFkSJPyKuuf0XXFEJm/LepFYz9jssm1UUIEiiYOqT6Sj8036+jYBMGZsG/H4EGAT48fdwNglquDgnMHuMOK31+1AS9gEZ8E4t+0JQEjX0B0q1O1Pr+PEyXbIf0eHHdIXe2EWnQ/dXUlER5LAlh7aZ6QJagWYZsy1zOzZs1m6+K3s93RzLHczBx0fjVdYHz58DFg4n6E1FZP3mHszUDDxiFmkzN1XfWXCbQWl7zOfJSdZ20hvd8UmQ9KhpOyNC7jjHD/G6dnP7dcrpSTlOOdaqbf6LWCpAluuv5HeYAHPD3OrgG0P/zv7OT3MHXIabikZP3t2Pe81dGV/hzlsB7puZBWxDFJSEA1LelL5laolLarytf7rV3DIaV4frSFjlUJiXrmMw65+Iu8grWuC4yfVIIRgUEmEV769iI8ZP8TIrey1YKKp+1QIzJztGZjUTZyMHg0hundTmRfRSRHMutYDlFfswNQT9KzXiPxnh2eVSZNfIKIXegjrcfMu8Sx79OBz8u7WmU+WgbTuH2ebIOFo86N1pbI5Y5npm4VtxNqOTUiDoUrmzrH7OKZS2ygrK6Si4kiKi/ObwGZeUpw9WsuiIX5+3qGu5cJB3XP9YnnClNOHleXdz95gzKQqwot3oTfGWLatHU2LYJpJnH9wmqZhDiRTsTw4KGRMCPFJIcQKIYQphNj3MigfPnwcdGiOh21wH/O3DgZKB6k39Cd33M1LTQ+yuWeFZxlhPSLrp430zNsdRkzODVO6Q1tfEreRi/SQqGdaPkzEcZzWEzx67vmUnXsOE1evYtwrL2cZcskpp1D305+gW/tP6t7wDUDXO8rK4ITupaQnuslcutk2znxxra0adaNCpE6i0dC3gZS2mjjdtCR28OSOu13bWrnq18SMboRWTigSoLzGXaUqdNubrb6qkMqi/M2vc1FZFGbt906m07JhMEdGWTi1CGklaqcIKEVRCxCRuS8LksA2SffyHbsNX8mITgtu9SetlSKLG0hvtAhGTu7ddobyWmAtlWG3d1k0D2HOXWZ3kDlh0eJIoF9n+TFhbwjUsDohdFLCt1oOoS1H+e3ufo9YzOvSD9CSTHPfTkW0ZUSdy1vOUKR68hD37wrpGqmcEH9Dh1eVKi3If18C/PTs6dnPD10xL/t51U0nIYIaMUdV5zV/WoqmKyuWTN6b+qy5wtPBiftO/j4oHCxl7D2UzvviQdq/Dx8+DhD0sE3AAvvgxn8w8eV7H6I92URD33qqwt4efqOKp1NYPphQ5P2pfcOmzHZ9lzl5RnqeBuWyaO/2cTyPZz+X/+Y3antTpjL4+usBEIEAE1etZOLqVdT95DZKTj6ZktkzAQifYHcoGPLwI4x67FEeHzGb30z9GABdQ8s9SYCe3qMWJlmk0EnGXmp6gHDxVEzrPmhPNqm2UxbeiyglR+hVBEI6kWJr4AyO5/DTruTT3//BXp2DPSFEiuKIrgiKlKQJEggmQGh0h3K8zTKZYFoCvXU3Sqkh+a64mRgRRGcSrTnG2rIqukc+TrZXek4VoUSwImAbzPZaDdhDQ3dXLLJ7dD61hWSr23qjuihMMJ3/Om1s6oGkut/Cz+0k+HYrKauY4llO4IW+Kn6zbRelpW5dpKz0cPdvsVSwz6/czNfWbMtMBGBsjQrTRoLuv/+gLrIedxl89xHlnXbF0bZS5yT5uTjjULvQ4dDh5Xz1uHH8+dLZFIR0NF14CgI0TZHPkpICxzQN06ry7hC9/HLTg7z77rv97vNg4KA8OaWUq6SUaw7Gvn348HFg4SxM+qiRsUAwyGlfvYbDTj6doqD9tvzxxEyOTk5GEzrDJi9439stLI0SKf+aa5p0kJaMLxVgqzF7WeEVwiYM1+5Sg3J/VgIZBENq8A0sPD477T+dIcKjRvHyGLslzpwZ0z3rbh80OPu5PN5FeqhS8AKWYWt3osW1/LRjDiUVt5WbkpAK8Tb0bciqE9OOV8nkI6eP4+iLruGK39zC0RecQPWIfhpF7yX0RqW6hHd0Egmq1qOiN02KIJpmMmzKdFYEcm0PMqqhW7EpLTa5+eOOhulWkcMX+S3h13cRWtrGoEGbSRkhsHzcRI6/VuaKHnHexWzTWrkv8gqvBtZgdHuLBMKT7Ptv2CSlNA0eN8GzXM/LO0jlVAumTBOz3UskM/la4RcUIRJJE31XnLSVH1mMqsB8ub2b6dN+61q3vHyu63ufFepudrreW/wvY52SW9kshGB1o7vKs7pYqZ1H5ckx2xt8+bixzB+jFFRN12jOMTJOWp0uPvvZy7PTNE1DSolEZtsi5e1beRAx4J+cQojLhRBLhBBLdu3qnz378OHj4MBJIYL95OwMZIybcwQLPq1yeGpMFWapkiWMMWsBSSjy/h+TY2fWUDPSHYIrMe0wZD5lbHdIj7G3FXaEqDZapCfZT7VnbyJNR1+S8qhSC17Z0OJZpu4IW8VLjRrlme/MaUvqQY9yttqyB9neq1ztI0URqkfO8mymLWErJAsvmJb9fPgpRxCO7l04cm8xrHQHYSvyFX6lmTQBurqqWLvDG3pLa4rExEMxzAL7/h1SE2Ooo9pPWGHAuLCvo0TQ1FqfJWP65h60nXbD8eZ25a1WN2YCceu6rdUbMHu9uWkiaO976KQpXHLHXXzyW991LSNTBkIXvFrqDptva8ufkJ6pks11TfmhULmGAeulYElXH2sTQUaPsltwtRoF1D73Tvb76h6l6kUcLw2XDlGkKNPKKFcZA5g9UpHxq09SxDJj8hrU7e1kqoLfLzRdoDe7rXRaraplTZPU19czatQoNOslURQFs0qu2Y/n3sHCB0bGhBBPCyHey/Pfx97PdqSUv5FSzpBSzqiu3jcm7cOHjw8OH2VlLAPNIpGLkodxUfzo7HRDpimrjfSzVv/QAxqfuNod9gm329VsLmUsg36EseS0cnCEgp3KWObk96eMLfjR8xxy01PZ7486nM8ziDisBlIoXvGNervizenhmy4s8hxn0ujl6YZ7eK35YbW9wjAf/7pdUftC498AWNe1xD7sD8gBXVjc6ZRx71EUtQnsOxyOITWWBbZQUNDJkUfdw2omsoIpbArvYIPWyOag+2VfaLq7eXWe7gXdlNARLlVWEkBgRx+h5ba3mBa0/LoSZrYdVK1ZjhnLU53r2LweDFFWU0sw4r73dt76JmZfGkMTLpL8xYVj8p6P+kpHHqJjn6I7xZzZT7laNx375hqKi20lcGvaXZW66O117IgnGR6xibNuHXSmw0M+z7/R1SqEOW2oO58s5jClzU3831voee6jhl714iFlmosvvpgLL7wwS8YqLpiQvX3l3hTOfIj4wJ6cUsrjpJRT8vz3rw9qnz58+Pjw4SJjH0FlLIM3dj2OhkYQ+ze81foUI6Yespu19h5mywSklVyUVxnrr7Q/Z8wIk+A2+QX1RVMZXf2RsZYeywx2NyqAc7dpCSEhiDgHOcf+TVN6wqnhwlJaEw2YFsGsGKKS86csPBWAxtgm7t/0A5KZ1jvavudL7QkBy6R00tCzqSqyw35/EJfzeIGy2RhWpJSrm8V3uUXciKan2KK3EBWFrrY70egwZo+q5HMLrNymPOf4z+Jinq4+CrMiv7IXLuqmzqjATKQxMnmDgrxkzEl6A0FvQrs0ZVZRE5iu61IYzp9vOLTcJmOuZuJpk8LCUawpdzejD0ccnSbytG/6w44Wehxmwa8tV9vMvIQ5bSzOnaVUwatPHs+fL53N4SPcPmJp0yRk3WdF4f4T+AFOnz4kr3VGwOGkHypX12BLr9qW07A2Q8a0qkhWGfuvIWM+fPj470DQoR7oe+lUPxCxqWe5Z9qgyfMYVJ8ndLcPEAjSKfXWrok8OWP9DA65if0hEtTiSIrWRL9hygy643kGf5FZ3R7QUtIkIARhJ+FyKEJmxmfMgaIKt29XaY3K+5p23MK8x1Ja9cFVstUElLo1tLycCaXu6tTNej3g7aUwbOgKBBAPun9Yu6HIxTWWaWlge5+3YjFtEol295vvdy8XAyATBqa15+1a6x6VsVxFDMB05JmFZZKAZWsxsqpQVVPmgZMA5YYq44bJKx09rmmRAlth+9+t3uren29t5rk2u3hg9VZ1DIGc33/K1Fq+f6YKRYcDOvPHVLlVRlTXhy9Yil5/x5/BHeceyh8/4w19O530Cy1V7vZ/qRO5avU37eWse1w63hVTqffXYPyDxsGytjhDCLEdmAs8KoTYjeOgDx8+BjJKi21fqoLQB6d6HAyIwIF5RIZLL1d+XJb8EcinjOWM81IXxBfUIkvc1gRBcgYRbc8J/B0x78Dz1zdVRZzTfT9pSoKaIKLlV8aU6at74NUdeUKX3fl7giGlUAweM56Lb/ulZ7+HnHC8Z9qBwlWz/85nJt/LiJoaIkG3SpsUIQaZpZ7a0IJoFyaSLSF3G6lQvv6FOaRXa47TLYr7JdKbxWhSwsCMp2nVbOIT74vzdHA5rwRWZ6dJE4oqVQ5Wea3X5kK6rrEksFW1qVowrprn1zR7lgfV7/Fvn53rmS4MSVMypY47lkZriaM1xeh2qF4taeu6xg1Enhw3JwzH719980n87FxvNwshBHNH2X59R46r4spjx7Dmuyf1q+ztCc4XiUkj3cpbe/trxGI7eObZ0cQTXwWUGqZbLZo2bdq0T/v8oHCwqikfklIOlVKGpZQ1UsoT97yWDx8+BiKEQ2sI6Ltv6zKQEQh5Q03GHkjOnjDnE9dy4hd+yGd+fLRlXK8GrdxqSj2P83pqegVEvGHfXY0qeVuzaEUooJHYw3F2x73bf2uLIh/lhfY1+3tTO0HhtigVOURDOmZ2d1UyZeEJFBSXcPpV36Kkyu2vVjl0mOv7OTf9iMNPPWO3x7o/mDhiHvPr3iAYrPDMS4oQg80yTzukll0j6BFxzJzR8MR8Cp6JJ3dsixiF3uKuZNQ3daM1qHBos9ZJ6zObeS9gFw8Y3Qk267tYFXAYxUpJZZ06X9FSN7HYfs1LtP/TNpttT9jXLJE2WNPktrrIIKBredsMiZhBd9rgkJRO5MUmQm+1EnqnjeOX2CYH46yUscgLjYRfzk/2MnD2No0EdVe40ok5DjIWDihD2H3tLQsQiSoSN31SFQUhL51pa38ZAClV4YppmpR9YqxnuYEAP0zpw4eP/YLmSHYJDsAGvHuLT//gDs+0pu29+7XN+Z+cz5SjJhEIqSquLBnLiRn9ifzu67mYIV8nkVBK5J099zM2GkZoYo/KWG+i/+rNf71jE4I+wySoCd7ptisCPaKPQ41YuXIBkeJCrrjrL4yd6VVgAE772rUAHHXBZ6gbP3Gf297sDcaO+RZHHvEGgUChZ15ShDCQIHJ9qQx2aV2YOfduYdBLEoQpiTzlsMboJ+0ouLaL0LuK7A6pW0mr4W4knrFXAHgw9Dp/D71GbFUrx597Bcd+5goq6oaSi8Q6tY2C6dVsjttkM5EyifRDaNp6k3nPd3BlBz2GSV+fm6Rvd5D2fmzLXJhuJeWPGZS/HVQuvnTMGM6bPZyffMprobIvKC5RL1CFkSC3HGO3i4qjpkvpvtaGYWAY76+S+cOCT8Z8+PCxX9AcythHmYyV1w72TjxAxEEPZErq1QjnPGd2zljOSnlCXyGSSASmqaEn2oiZJnHkHnPG8rWgARV2bOpyqzpBISh2FmLkHodwztIIRnavho6bPZ+v3/8IM087c7fLHQhoWoBQKE/rKinpoRgTE8N0ExddV/lb5l5c6twm4kLK3bezSpmMHv0WuYl2qwLbs5/btV46tT5iJOn+zXrGVh9u5zgZks7/bHatWzRvSNZKA1Tz95+fZ4cF/+Fwqc8t3Jgzxj43P9/aTCy3sENK3uEwuilmo9sxIi82tvRSWRjqVwnLhaYJbjljKmce5iWb+4ICizAbhskghz3KDzarwgQjbZPesvIGTNMccJYWGfhkzIcPH/sFpzK2tw/lgQiRx5Zj1KEHxk5H03W6RYx0WhGX/K72uUlj9scTKks4rbqEc7gHKQVSagjNZHs8hdZn8O9lDbT3eo1EM+hN5m90ns4zMElgSrFta2AMdatMojfN1fJm9VlIgnna7QwEDC13WDOY0C1KMDCy1yADYZGxULTPNd2UztCbujcyald23a4UpPonY+N7lct77l9FEu/1+Hv4NQBSjbYaG1vRQvdz21zLiZDuKr1MpA3GO3y6DhtezoOfn0dVUZijx7vDxocNt0OvTzd3sCOWc8+YsIEx3MY1kDIJP+uwQskhnaIzSXc8Tetu7rsPGtGQImOxHLPdhu0q966n1w67Tp36jEsZCwQGVg9dn4z58OFjvyAc+U8D851z37Ft5csHZDtCCDpEH8uXnQDkKmNqqB4dVBWS+Yb2sKZx55jBVNIGUiljUqYZXWCrAasb8+cNgQpl5YORxztrcyzJGYPsQfukunLix9qqoZCScawmFismmSwgsAdbgoOFmpIIXzjWqg40My2P0p7WVJnG4YWlbkNc55n51QXu1kAZBLb1EnlOEZb6Km9odK2WafLtpmNl0rtsygqfOs1f83mbJWWKdNoOJ1536iTA3Wz78BHlLPn2cZ4ihrKIfa1E0vRUWGKYlFUcTQN1aJ1Jd0eBnErSzxQc/GKd4qAiVJn+lIkjVCWvXq1+d2PjP13LG4aRVcYGWrjSJ2M+fPjYL2iOpP2y4MB623y/2NG3zvU9ndxNr8L3CR1BPF5CU9MoNxkDTFMwPbSR+MJazEGWrYFj7GvZ2cNdX3/BmiyQUmCkEmyI2cf3qxc2vO9jSjsG+8RMu0m3EIIvDh/EPVNHMrGwAC2g8cvzrVCYIQmQZs3q+YDIW/gwUJDpPJAhNRuDO4jr7muaFmrgbmpzFxt0OipQQ3tRVWvmCVdqnWobigBKSkqa6TfRLLOOMxE9j9D8zGvPk07bytqISkXs7rtsNou/eexut11T4rDMMCSi250zFtjQTbR4KqFgmfcwc5LI/vzcxt3u68NAfa3KVRs6RBFDWRhA6oJSOjzLplIhTNPMkjAp5YAKWfpkzIcPH/uFSKHdP69wPyqjBgJebvoH92+ym1WLA/iE7LYaZpumlidnTKBrSQjpeQfg1wJphMgMIipMmY51UeowZ31h7S5efXA9Sx7b+5L9VNqkLBpkzrQapMO49M7PPcuRb68huOJIzHQnJg5CYkp00raBbWjgXvOI45jLZSuaZpAMapwvHswuk9bUC0TcdIcvVzTYPRX3puKvrMCrEAZXKlKQFAaVlduYfsh/GDFiGak8HRjGpZX66FTGRJ79bt2xlUBArX/h/Prs9Ggo4CZbeTC4tICPTVe2GaI3TWCbu0AlsLWXn29tdh17BsUvN4Mp0XbFs70uDza+MnUY518whTuOUc+gV2ZPAF0QMrwvUYYRdCljAG+//faHdqx7gk/GfPjwsV9IO9jDR7QbUr+YcvQB9MSylBMpNY8ypmkmBRWqSk9mCETOuRx35pXWdgThcIyKEas55Vn3gLn0qa0sfngT0pSkkrsJw4xWrYIO/+7TdPSlPKalEz51Gd18D8PoZdc2NWAZmWbYesb6Qv2/lsctfqAgYzQqpAoNFxR00z3Ofe7LBjUghIFhdV745NzhANx+tt15YW9yITO9F3ORTEZIkkbT1PUoKm4lncdnTlp5YMLh25Zs6PEsFwgGs3Ul588bscfjAjvRfUhZhCsso9XAZu+2AUibtKcNRDynGblhovWmCazpdM372bn71sroQCCqa3xvygiKQ0TGVnIAACAASURBVIpQj45GELoAzVvEIYR0KWMAXV1dnuUOFv4/e3T68OHjw0bKEc/QPkDbgg8Ti3c9yobuZYydPW/PC+81rLwlU3d5s+U+hdMTSkmNKcGstlWOBfKZ7OdAwE6YLstNwLawdVUby5/dlneeURUmFXbvtNWR4H/0NqWsFVSqf6VQPSU/v3MnZVMrSU5SuUlZZWwAh6adyliaAJMmP+fpC/qSvoD6kUvpLlbK2KH15Wy+dREVDv+1fLl1uXAVDDgQD4VIiTSmo4oznzKWvSMs0htf00b3M+7G5gYmQghMMm219u7vLVNNW1oQpM46Tq0j/72jb+3fzuUX44d7iPvCCYP6WfrgQOgCLYeMFRefAkiWL1/uUsaiUW+XgYMFn4z58OFjv5Ay//+opgS46Ec/B2Bzz3ssaXkCXT9wREOzxgBphSkz5qnhiWqQNjOP44CGMbrYZasRcFTfmdJ+bAdEfmf0F/+6lo7GvrzzjCFRz5N/VUz5GBy9optLhv6va55u7bvXlDQOiahQKmQr+sQH1PT7QCAbXrTIWDCYpK/H3bB6JVMoKmrjRanaN+XLD8vtY/j7y2d7lunv3v8eN5IsaM4qYxUVDWzVW5g1+0GmH/K4vQ+LrLc/uI7t17xEyx9WeLb1h8hzNDY2Zl9/ctsQ9Ye6MkXAisKBPa+TUXALvCHSQQGdqSVu0lmQx4/tYEIENJI5Vi6aCCCEyZIlS1zK2LBhw3JXP2gYuH9FPnz4+Ejg0BK7MuyjroxVDa/nyj8+kP0eCB0424aMk31DwwQ0TBIn1BE/sY5AqXoMy3zJYhacVKC4bWL289xFdtucyUk9y9+6dsVY/Xr+vB5zcBSZc50Cm1TI6hTxD29xQa/XwR0gGFR5OR+kiev+oiBDHA1FxoDsv6I3hehJMZ8XAZhlKGuJYQXegoRDhrnd+IN5CKiuCUZVe6skt4vhdIVb0AM2cda0FOFwHyUldgVntjNAbv/LPMjcK3v78vPA5+dy9//MRAjhOfYRdblVkQLRl0bEvOrdv5ftpCuntdZAewFLaYKGHLsNoQWyhssDKWnfCZ+M+fDhY78wJE/i8kcZzibN+Ro27ysiRYrUJJNRF+HJhCzN3TyOh2C7vofTttt5Se2LmCX2+b/il8dQVK7IRLPmHnSM8hCDM/ldOeNneqTaZmGpOywGLksrSgw4su91ADo7ajgxeYhn+YGEjLVDcG0XaavXYiWKAIVfbib8SjMSQVlZUzZOmE8ZC+QQmHzFlbomuPcSr2IGsJ1Oxo5dnP0uhJdw5bZpcqJ44TCqrp/pWFhdwMBeEuHBpQVZz7Fc8lRSFGLzrYvsCUFB6I1debdz3xtb2dYW26t9HjQEBKRNDjv0z9lJmoOMOZWxXMXzYMInYz58+NgvODsZ5jMR/SjjQNo2SEdpppOMZXpMypzH8efkHZwoH+VaeQMn8mh2unBU/e3c9muSM6sIBjQGj1HqzSeungHAhqBb2TBrCxhdYRG5nEHctCopp8890nvcjuubSptopiSdDiClTqW5d21wDhYyITStI4lYH1NnOoe/pFDnMy0t4rYXYddgnkqVkkgwr70F2Pl1GWRClq5ldkPGSk+sJ5my1Z7M3bO3YcrdQVjb+MaJqp1QcFUnIrF3f8e/usDbEPxgoyISJCShvHxOdlpADyEsUzWnMuaTMR8+fPx/A+d4UFk4cD2n9gUHMgRXGrJzbRq2eSvvcsOUhfRyIb9nCu9mCRuAwCZjQVIQ0CgsDPL01lZeWd9COqRRP7VSKQROaIKeiMhsxI1saMybgxYo7LQX06CgsIVAIG1tZmCFqHIRcVQmioTJjp3jPCHaFEotzLRJ2htPsVzLk6XXHU8kqFNqqcRftCoW+8PQoSuzn4886h6OPOoemoKdeZetumQKq1atornZbtad+Q17q4ztDjGLkFx25Kj3vW5xZOCp4kXhAGaOJ1pBQWFeZWwgwSdjPnz42C8krCbVBUF9rway/1aMr7Zd7BsabDKWUckW8CzT5NuMksp41uyP6BRFeWfxJwA7sT9h2Vicf9dipt/0JJPPHsOcRSNdq0lNsH6EFXbNJWoWGZOmImMFBbZlgumwYZCaiW4d79T0cAoYmK2QMnA50KdN0jKE7E8Zy5CxfpSxi+fVZz9Xh0Ismmpfz3Kr8rI4EmTFjSfytePH2SsmDE9YsrjEGwY0A53cH3qVTuEuvIiMLef+++/n3nvvBWDOnDkUF6sihH1VxpxhyQlWQn6+v91hFQXcePrkfrdTXTzwXr7CQQ3TeiaNH38zE8Z/DyF0T87YxIkTGTw4Tz/agwT/yenDh4/9QnufCp8snHBg+jgOBFz0o5/zsW9cd0C3Ge4OoVuVkNJ0KDZIXn3h0xTRw9V8j3JU/8P+Evp1rYBUvMRaFwIyRSzm7nV421NrqSxSA6XMqEMatBRYDagdA+/4SZWYNWpATiX7EERpWmareCY2oZG6lq2urDeqqfl6/jZBAwVOMiaSJoYmPMpYkiASWCWnABDs54XiBgcp0TT4H8tw9e7/melarjAcQHOQpNDbre7EO3DZXGRQO3gd3VqMlfp2zzwnxowZk9VJ99baYncYFu2fUA0uKeAiBwnNRW3pgcupPFAIB3UwJFJKhtadR13dOQiRyRmT9PQ0Mnfe3zj55IkDqj+lT8Z8+PCxX5g7upLakghXHjv2YB/KAUPV8HrGzMifjL2v0KSWzQuS0v3oNRxjaiahPzeHLAM9FEFzzAvkCS3+e1kDSUsdkNGMFYVjJw5lbO68YVlvq60r3yHZl6Brl90Q26nQpdGyyphAoBcOvDCVEwUuMmYgdZHtRZmBiU4XpdmWSf0pY07ommBGfQWbb13kacadQVWRUsu0rhSthYo8Z0hUX1+pZ/kRI5YDEMi57rlhNSG6icdVyFLX952MHWP5gzm7C3xmvltNvfpklUf2f+fkL9QoGYBhyoy33N2vbs5OE9m4smTXrpcJBBJs3vLrD//gdgOfjPnw4WO/MKg4wuvfPJYJtSUH+1AGNKQmsoOxM6E7E2o0LbVMy5Ix70Db3FxPMBwiSZqV7xwHQFzkN67MkLEsCXNszqmMvdNlh8WClauQpsBwhB9zqzw1y7BUmxRFiw68wdgJV5gyYSJ1me1FmcFGRqvfmKmm3Esytie09DjMecsb2cQoLhAPsoYJ6HqaxczlHewE+L5eRdB0J1EXXpf4ltbbswR5f6xkiiNKFXKGJz93tJ039t1zp3P4iAoAPnZI3T7v58NGpgDjxn+vRErJQ0u3kzItOxMhs397Uqb73cbBgE/GfPjw4eNDgBAwxqwB3MrYOHMtADt2KP+wKSiFpNZhZ5HBzp3jKIwUkhYGrV2D6dmZ3/UdIGlY7MJSfKQjmZ2wTmpSGY99+Uhe73Q7rktTI15pm2HmkrFMmLJs4tD+f+wAgZM0CYCKBFrIrTStEZP4J5/Imp0Gc/Pp8m13L0jQBXOGZz9XFO9kHUplepkF6HqaO8RV/Eh8K7tMR0ctAAF0IhMqCA4tovZbs3nyySdztpzIEor9IWOZcxN2kLFBxXbYMZJj5rr65pP2eV8fJpzX/M3N7Xz1/mX84lVFKoUwHWRsYCXy+2TMhw8fPj4E9PV1cWRqIkONSpcy9qnk/YCtlh3DU/xcXsIItrjWf+nFC+jqrCEasZWwosH9ez5lCiuyKljYPbgawwoZXeO1pjACYYqLW7Pfq3Enm2cS3vWPYFP42/kGT3IKAWcTbCl5Wpz0vsOUe0KFo7K4L1ZMqZUL+Kw4gerqLZ7lM3YXOhrBwYXUfPFQ1m/fyKpVq3KWC2W7MOyPs0Xmdwb6CXUW5ZCxXHL26jXH7PvOP0AEHQS1N6FeHP65Qt3nShmz8jZ9ZcyHDx8+/vuQTMbQ0CiU4ZwwpUWarEFCAOW4G4C3tAwjE2eMFPevhmUQDmj0dHcjBaSmlZOaXIaMepOV0w6fpTvlJQBEo92uBPP5vMg35fXZ7w0Mpb29llgyvsfjGGjoEBW0xUoJbHOogdYpEKb6uDui9akZSg3MJSb58Nmj7JBfPGi6cgDjeJPmMz5YOppqdg0kEgnPcroWRKJC3vtjvVJlFXg4w6kAdZWK7A8p2H2l7JCyPd+HBwPO69fY5b5H3WFKXxnz4cOHj/86VB2lChx0NEAwRS7jIvlbkAJNCo8xqBOZgRog7CBj0sy/zhF1Ye59s0EV8YV1jKHeNj0AybRBTaybqY1vU+YggDt32sUYApjMe3xp+CDru8nqVUcxdPBHJ48IQEYUgapsc7eJEr2WQmJKdF3sluDceuY0Fn/z2L0iY4XhAIeNUw2rdc3kET6WnZev20LGekGXGliqVe6xVFZtob3jeaQUub697xuZSsjWHjfhC2fDl97fGNyPgoEPC7ojOfL6f9n9PQ1Ts8KUGWXMJ2M+fPjw8V+H+mOUBcJIQ5Gaa7mJE3gCgEXJw/ZAxmwFK1Jkk7F0Or960bRjB0V6/+7i1bIJgAd+eDNGIEhAuisy45Z1Rl9fMd27VIXd1LBS1pKECKWL0M2P2PBhqYCBqNtdPrDeSpA3JeE9hCg1TVBTsvd2DoeOqQLAQGOTsI1gY0SVt5sp2YaVnycynRjIKmO5mDTpRWuZ/SdFZx5Wx+nTh/CFHINa0wrX5gtfPvGVo/Z7vx80nJcwmzcJ/GP9qa6/o3h89xYiHzY+Yn9NPnz48PHRRq0sw1naKBFM+dwCerqr+l2nosJO5o8URZmTUsrV6tXu9kWnNj4GwC6KaEv3r97UsQ2A6444i5ZghNKqLs8yS948nWXvnEyyR5HHJ2//HqDIWB9J9NKBZ/i5W1jjcG41pSy0Ku0S5gFvet1pKvXlZbnANX0t44k83UD4pSYaUc3es0RBSEzLN2758uV5tyul8HZReJ+IhgLcce6hnnDjZVZ4tS5PGHJ09cBufwX9dyV4YvNxCCGz5zke3/FhHtYe4ZMxHz58+PiQUHLiCG8LISkIjyhhcv0ZLF58Jm2tKvyXSuVXvQrKCpkWUQNmPO4OP1789a9QndhFUz+KGUCl3MXhvOmaFg7YeUPr180CIBYrJZ0Ok7IUpSl1KuSzkGcAQaDso0HG/vA/M6muKMgm6BumO3dOhnRIm+hNMXriBzapuy2uFMelHYeClARWdUAszWOcDoCIG9wu/pdr+IlKWgPaRS/PrHyZRx55hPXr1+fdrkrg/2BChufPHsHmWxf1G4r9+XmHDsielBlMGVuJ7C+cKkyPAe9AgU/GfPjw4eNDQsnC4UQPy28SGq6IkkwUZkNQmzcdmp3X1GgngwcKQwy5bi6gnNyvkLdn51UPGUJgD1Vig9mBjjtfJoQiY73bz6KjYQozU6Oz8/qs3Jqx0zfxZ3kWc3h1j79zIGHh+EHMGl0JEqKyB4MckiGlozfngYXRrchYYFUH2s4Yga29RF5sog83id4mRqBV9FFa2si7gS0s71zPkiVL+t1uvobnHxZOnTaEk6YMnDZCuSgpDJE41nt8o8s2IbKlDyDEwGrl5ZMxHz58+PgQUXrySKakHT5eUg0K1dWqnVQmdyyVirBu7Ry1jKXmfPGTlyGsUNpZidmYZoD5vJTd1pNtXZTU1Ox2/+NZ7SFjmWbZSzdF0K3/2cfnHiZ2l9s2UDG0IARSMpPFGDKXjAEfkFgyrVRVJoqcfQwzN9lfLMVumzacadOfYsiQ1Z7tlJU3cP4FJyNEAAmktbKDRsYGOkwkudUNZjTAOjmOYFDLWohkXX4HCHwy5sOHDx8fIrTCILPSdtJ0Z6cKC06cOJFLL72UsPXGLoRJc/NIdu4cw+bN0/nsnHOommxXME685hiq0hWubV+3oYE1nbt/rJ/GQx4y9oQ4FVBES9P+X3t3Hhxnfd9x/P199tlDK8uSLBvbIMs3IB9gsMEGgzECgsEhhBwcYwgpV0pJh6TphAAZkjadCUlnkqZN0hwtOdq0JJM0E4amkxIIA2QSzgCBAMXmNGBs49uyjt399Y/n2Uu7ssFIep6VP68Zj/Z59tndn/Ynab/+Hd+vR8uiitG7iuAr35+u2mnZKPyEYS4IOvNuSIqPgsMKoxONVSZUTT1VLjH1sDupdNvbGqRf+O9wt2Ums6fmeRYvvpuNG6/CuRwPtn2e1/NtoxU/Nrxitpa+1dPK55oSUID29tZSMOacgjERkUOWeVa1bqx3X3fpdmdnJ7u3LgNg167DKBR81j9/Erlchulrjq56Hr81zSaGfHDvZwH6le5b3PLqDSTJlUoaFV3lvllsHbtcL8lMeQqncgeaJWrrajaChOeBgwGXIjdkZMwc+M/XbmAYCVedOqfueeuveP/DmGA+QSWG4d7fQiEoW/XQwMzwSUamjeNNKcSqTHLsGxQcZ599lkbGREQkUBmMFacnS5qP5v77LoN8uZh01g23WH7IJ/J+/qI3s4dVxy8AKBX7Lupga9XxG7s2V7xE+VrPK+AaLaUFkAyD1EdYzo5CW9V9/gu7SWwKKhl89ORZI/q6wy2Ct77aQKBUb9KrDpTPOae6DFHGs2gXjcVcwdUZM/SMpBtgy5bvVr2/g4Pba6+NSOP9VomINLhJ68qjXGvXrq26z08G67dSTeUAbCqtvC11RsbmumDExSPPm5vvAILArNI+qouNZ/rKU3mVI2N4gxScxwVuxdtrT0wkirvrHLj88EHMaUdOGfa+EW3Pi7vLB4VgA0FxY0Flgl+ApUuPrTpOe14wF6dYrK6OVG2liVQiSJD81rZ7yWbLeeJee+3HY9m0/VIwJiIyxrKLgw/9wcE0qVT1rq5584L1ZBdeeCGTW9oByA1TeeacFWdUnzCj7/TyWpmB4zvww8LeXsVoWAu7qx6WojoL++oLzio/5ZDVSc55dF9Xnd8s7oojkbZnEMsPPz2V8sfmIzHxVvn9Tv1xO5lfv05/mI5k587qDRj5fPUUaiaRCAYrRzgn2njxviltfHvhzKpz0zJeqVrFqtNWls7n83uJCwVjIiIReOzRtTz6yHk155ctW8YnP/lJurq6WDJzEQCv9m2uuQ5gbveRtSdT5akxl06QDNNWVAZjaco1+/7KfZElPMbmzbOC1+8+jvRhzSzKzeDcaSuZ6lqqnt45IzmleiQt7jZsCUYCU49v228ai5FO+vpO7Buon9m/r79cvukhVnDH1hSJ13vHqlkNx8w4/7DgPzF9PdPp65lOMuFRXK/vCuXUL6nU8ImWx5qCMRGRCOzdO4nBwdohLzOjtTWcljxAbNDUVr/mZOm5yJcKVFfuoJzIztLtpTyCAc89eyonrziZcz4U7Kz8wC0f5YSrzyTb2s1Q76ZAdRRKuxoLDttPMOZF+H29vD4cEauYFp41a1bVNd/kevxngr6zvnjVVoybZ05ZBEkPkh5+IllKLeIqSn+1th43zKPHnoIxEZGYmrIgSGXRs+r0uvdX1qmsx3kJdhOMbLVQnu4a3NPMl9z13L/II983ha1bugBY3bOaRCIYWfNSCSxhJAtLeOjBD5Qem82WA7lGUSp6nQ/WZ3kePPO3a2quizLGTGdzYRvKwdh5552HK5SDh0FL4e0b2SoB41V7srx2zPcTpc2ThYpgzMUoQYiCMRGRiMyZUz/1QdFR3Udz2WWXccrq+mu0EokETz5xFgPLOhicP7F03quYbltAUMZocsWOScPRyUZe+eMFJDJbKBSCYMX3axc/U4D+/mZeeCEogdOW2f9oXBwl/fD9CBfLp1MJmlK1Ox1HOxa7rmfesPflXYI+0hiOpUuXctFFF5HN7uPRxy6qvjA+8UPD8BNBahPnqqcpqbfzMiIKxkREInDTTTexbt26A143d+5cPG/4P9U7d06j0JEhP6eFW90naHdv4cIPGc8rcAk/5GvuY1WL9msWiYfBWL3XKYTFrvf1tobXNO7IjDmwfIHUMCknRts1q4YPvl9znVxp/8FzE+aQzWbp7u5mx46Haq4rtCZHs4njkh/ups05H1dVLiw+wVid/waJiMhoG7qLciT45PDJUUgYlnPk/SQ++apRsc1vzmb3no6qxxVHxupxqSBA6+8PF+3n47Po+aDkHOk6wdglJ85gyYy2Og8YGW3NKVrqpF0oCasAvNA8szRVPDRYsB0D+C8HOwCf/ULtNKtU8w2SZvjhfzJyhUTVNKXvtwz30DGnkTERkQZ21FFHlW775EgyyMCJU8jNmgDJ2om3VLq3pr5kIe9z7bXX1n1+f3oQhO3dO4knnziL/JvnjmDrx0hlTJOvH4x98QPHBNNZo+S2q5dXTR8DnDSnIigO25igUBqh3Lt3AwC7mEgvTaQeCYNqGz6hrJQ9f+ox/OmUxSTDfs0XEuzY8RCJxASOW/JDmpuHnzYeawrGREQa2CWXXFK67TOIzyCuJUnuqNb6K9Kd1WTR7+jYyNRhCoxXTl3u3DmNRH7kR/RG2yUndpVuW96RDkf7ju18m8l0R0BTnRxm7c0VU44FB/15Mqk9DOauZ/36L/PyK98G4Fr7Hlfbv0NF8lo5sKaER1PCI1kxTblnz7P4/gQmTVp5gEePLQVjIiLjhE+OV2x21bmdO4MEsy++uIT+/iwbNiyjY+KQTPN91Y+pdMIJJ9DVVQ5m+hkc9tq4mjW5mWM7W3G+Qd6VRpXGMqbJhMHY1IlBZYVLV3Rx6YogOanveyTe6idz7yY275oA7CoFYpVsIF71FBuFH773g4Vgmtgsfiu0FIyJiIwTSWoX1xfXg+3rbeWhBz9Ib287zptYdU3/1vnDPmcqleKKK65gzuxg8XnusPh9kL0d7c0pLOfwdg+WgrELl80A4OGbzxz11y8GY5eH9S+b0z4nz53MS7euJZcrlPOGbW/cDRJxVZymHCgEo7oKxkREZNT4dYIx57yqrwCz5y6uuiYz6cDPvfiY4DE2RiWDRtpjL5eLQmfCtBaXrpjJi188lyktwxVif/eKo2+ZcFH+uuUzWbt4Oh9bNbfu9Wnrqzou4MFAHvqV5PVgpcJpymIw9ru+uQwW4jXX25i/VSIiUmP3jo6ac8XaksVF+wuPXkA2Wz1N6SWHn6YsmjgxGE2bNOltRG4xtKuvHKhWLuAf7WoCs6dOAKA5GXzctjYl+ca645nUXH/t3dDm5EiQ+c0mMvduqnu9HFhxY8agS/LA3pP5p1+dz9V3PR1xq6opGBMRGSdeWH8iX+v/89Lx592NNGfDxcvFQtR7dpFMtlMoeLzxxjzuv+9S+u2wAz73nDlzWLduHStXxmvh88EYy52IP7/mJH501XJS/vCvecysckqNXL56Cq1rzqdrrv/uR5aNXAMPAemKacrX9hwOwFPPb4uySTUUjImIjBOrV5/FhEK5iHSKfpwFO/bmzQsy6Pf29tLU1MRvH1jH+udPAoxt2w78wWRmzJ8/v36W/gZTL/v+aGlvTrFy3v5zs52xeFrp9oTs3qr7BptPrjruOWYaZy2ov/NV6kv6xWAsie8FG1Dy+Xhthmj83yoREQFg3rxuNm8pT38Zjh3bP8yuXQ/Q03MqmcyLdHd310w1Ll++fKybGql6ecai1J4p91nSr17352W6gA2l43nT4pOotFGkKqYpk2EFiYLWjImIyEj6C/dVVru7SCazNDWVF6p7FOjvb2LTpiPxfZ+zzz6brq4umpur60sODjZeuop36mfXnlS6PTEdr2BsZsUGAldVIdMYGDKCMzGtMZR3Kl1KbZEkacHPetyCMfWqiEiDW8kDrOQBUqlgvVjC5cibj4dj7759AGSz2dL1ZsaqVavIZDJs2bKFhQsXRtLusbR0Znk0cFZ29HZPHozWpvLIWKFi1+vyE3/JE33VwdiEMZxiHS+KqS1ITMP3ghqt+byCMRERGQXJZBMAhXB0JUU/ixcv5u6776atrbruYk9Pz5i3Ly5SMUvP0ZIpfxQXXGWw5egfEjRM2F99S6kr7Qe/D70DvVg6eD/jNjIWr59IERE5aJ7ns+2tI0iFWfKb2Mcpp5zCZz/7WTKZTMSti94RbUGwmhzFGpQHY3JzeaQu7zwSiWAUM52eTu9g9RqylphNsTaCVJjj7ZmtR5dSvBRiNjIWr59IERF5VyZNuoFbuJk17k6efXQ1ZjYudkCOhNd2BFO2vhevj77WbLlGZcEZnZ2Xc0bPBpLJifzyteqdrq2p5NCHywEU14w9+fo88uHIo9PImIiIjJbTTjubWbzEZXyPC95/QdTNiaWUP7qJXt+NgvMwCwKGe97axc83ba+6P6s1Y+9Y0iv3d57g/csXlNpCRERG0LHH3MHOnesBqkbB0unscA85pCViNjJWaY9r4bs7pvDS4xu4d/tubEjMMJYJa8eLYrmrOdMmMHv2X8OjT2uaUkRERtbkyQuZO/f80rELP2c8T//frieO42JfuXgJAOvdkXx/50zu3R7s+it1Ziizn0z+Ul+zn6AwMYmXTrC9N0zj4sXrp0DBmIjIOFMoBB/YTU2tEbcknka5HOVBOWfx9KCK6NABmyHHmaQ+tt+p5oQHBs/t6WPXvjAYS8Trh0C9KiIy7swBIJutLRx+KJs7JUh2azEcG/OMYMhuyEiYDR0Z05qxdyyb8II3uODYV0yiG69ZSq0ZExEZb05bdTtbtz5KU1N71E2JlSUz2tmwZS8dE1IHvniMJbAgYBgaJAxdM6ZpynfMN8OZYQXHQK4YjMUrGlMwJiIyzqTTbRxxxBlRNyN2bjlvAWctmEr39IlRN6XG0JExb0sfLu3VBA3JmE2vNYLp6SQYJIDB4sjYvjxv9A8wPR2PwFzTlCIickhobUqyZtG0qJtRlwGWc/gv7yXzq9dIPfYW6d9tYU22uo6oxXHBW8ylPI+WZIJmz2OgYhfllx98McJWVVMwJiIiErHhgqx7fvvqGLdkfPI8o1Bw5ZExYOObeyNsUTVNU4qIiMRcS8bHj1k6hkZinuGGBGO5wfgkflUwJiIiEnN3/uUpzOxoPvCFUteOXJ7ErgGeX1+uGyONzgAAB6lJREFUaHD6zEkRtqiapilFRERiLhezWooNJ4x2eotJX4HDO+JToULBmIiISAwsWnzYsPepDNK71JevOZWPUXoLBWMiIiIxsL+0FUe0NY1hS8af5K5c1XH+8Cyzp06IqDW1tGZMREQkBny/dnzkpnOP5rxjD4+gNeOL7xkDFceDi9uZPSETWXuGUjAmIiISA8lEdTB296dOY+6U+IzeNDJvyKjjptOXRNSS+jRNKSIiEgOpIQGDUlmMHC8d7zV3CsZERERiYO+QBeXaQTly+mP+XioYExERiYHeIcFYa1MyopaMP5VjjLkZ8cvXpmBMREQkBnomBwXMs9OyPHzzmUyekI64ReNUDGd/FYyJiIjEQDocGMsMOqa0KBAbSdMXdpQPYjhjqWBMREQkBialgmnJ3Tv6Im7J+HNY10QKLcH7m3i9N+LW1FIwJiIiEgPLZrUDqAblKBgouNL05LFLp0XbmDoUjImIiMRAPtzxp4wWIy9hUJgcJHmdMbM14tbUUtJXERGRGOhsD0oefbxnfsQtGX++vmAmy3bsIdeZpSWG6/EUjImIiMRASybJS7eujboZ41JnJsWqSS3ct30P92/bHXVzamiaUkRERMa9p/bsA2DDvv6IW1JLwZiIiIiMex3JYDJw7ZT4rRlTMCYiIiLj3m2LZvPBqe18a8GsqJtSI5JgzMz+3syeNbMnzeznZtYWRTtERETk0DC/OcM3FswkGcPtqlGNjN0FLHLOHQP8H3BjRO0QERERiVQkwZhz7n+dc7nw8PdAZxTtEBEREYlaHNaMXQH8T9SNEBEREYnCqOUZM7NfA/VqDtzsnPtFeM3NQA740X6e5xrgGoCurq5RaKmIiIhIdEYtGHPOnbm/+83scuC9wBnOuWFrqDvnvgN8B2DZsmUxrLUuIiIicvAiycBvZmuAG4DTnHPxK58uIiIiMkaiWjP2daAFuMvMHjezb0XUDhEREZFIRTIy5pybF8XrioiIiMRNHHZTioiIiByyFIyJiIiIREjBmIiIiEiEFIyJiIiIREjBmIiIiEiEFIyJiIiIREjBmIiIiEiEFIyJiIiIREjBmIiIiEiEFIyJiIiIRMicc1G34W0zsy3Ay6P8MpOBraP8GjJ61H+NTf3XuNR3jU39NzpmOuemHOiihgrGxoKZPeKcWxZ1O+TgqP8am/qvcanvGpv6L1qaphQRERGJkIIxERERkQgpGKv1nagbIO+K+q+xqf8al/qusan/IqQ1YyIiIiIR0siYiIiISIQUjFUwszVm9pyZrTezz0TdHgmY2W1mttnMnqo4N8nM7jKz58Ov7eF5M7N/DPvwSTM7vuIxl4fXP29ml0fxvRxqzGyGmf3GzJ4xs6fN7PrwvPqvAZhZxsweMrMnwv77m/D8bDN7MOyLH5tZKjyfDo/Xh/fPqniuG8Pzz5nZ2dF8R4ceM0uY2R/M7M7wWH0XQwrGQmaWAL4BnAMsAC4xswXRtkpC3wfWDDn3GeBu59x84O7wGIL+mx/+uwb4Zwg+/IHPAcuBE4HPFQMAGVU54FPOuW5gBXBd+Hul/msM/UCPc+5YYAmwxsxWAF8Cvhr233bgyvD6K4Htzrl5wFfD6wj7/GJgIcHv8jfDv7ky+q4Hnqk4Vt/FkIKxshOB9c65F5xzA8DtwPkRt0kA59x9wLYhp88HfhDe/gHw/orzP3SB3wNtZjYdOBu4yzm3zTm3HbiL2gBPRphz7g3n3GPh7d0EHwpHoP5rCGE/7AkPk+E/B/QAPw3PD+2/Yr/+FDjDzCw8f7tzrt859yKwnuBvrowiM+sE1gL/Eh4b6rtYUjBWdgTwasXxxvCcxNNU59wbEHzgA4eF54frR/VvxMJpj+OAB1H/NYxwmutxYDNBELwB2OGcy4WXVPZFqZ/C+3cCHaj/ovIPwKeBQnjcgfoulhSMlVmdc9pq2niG60f1b4TMbALwM+ATzrld+7u0zjn1X4Scc3nn3BKgk2BEpLveZeFX9V9MmNl7gc3OuUcrT9e5VH0XAwrGyjYCMyqOO4HXI2qLHNib4fQV4dfN4fnh+lH9GxEzSxIEYj9yzv1XeFr912CcczuAewnW/rWZmR/eVdkXpX4K728lWGKg/ht7K4H3mdlLBMtueghGytR3MaRgrOxhYH640yRFsGDxjojbJMO7AyjuqLsc+EXF+Y+Eu/JWADvDabBfAe8xs/Zw4fd7wnMyisI1J/8KPOOc+0rFXeq/BmBmU8ysLbzdBJxJsO7vN8CHwsuG9l+xXz8E3OOCZJZ3ABeHO/ZmE2zQeGhsvotDk3PuRudcp3NuFsHn2T3OuXWo72LJP/AlhwbnXM7MPk7wBz4B3OacezriZglgZv8JrAYmm9lGgl11twI/MbMrgVeAD4eX/xI4l2CRaS/wZwDOuW1m9gWCoBvgb51zQzcFyMhbCVwG/DFcdwRwE+q/RjEd+EG4e84DfuKcu9PM/gTcbmZ/B/yBIOAm/PpvZraeYFTlYgDn3NNm9hPgTwQ7bK9zzuXH+HuRwA2o72JHGfhFREREIqRpShEREZEIKRgTERERiZCCMREREZEIKRgTERERiZCCMREREZEIKRgTERERiZCCMREREZEIKRgTERERidD/A7Q3VRQHygl9AAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"nComp=3\n",
"reconst= pd.DataFrame(np.dot(pca.transform(rescaledDataset)[:,:nComp], pca.components_[:nComp,:]),columns=dataset.columns)\n",
"plt.figure(figsize=(10,8))\n",
"plt.plot(reconst)\n",
"plt.ylabel(\"Treasury Rate\")\n",
"plt.title(\"Reconstructed Dataset\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Figure above shows the replicated treasury rate chart."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Conclusion__\n",
"\n",
"We demonstrated the efficiency of dimensionality reduction and principal components analysis in reducing the number of dimension and coming up with new intuitive feature.\n",
"\n",
"\n",
"The first\n",
"three principal components explain more than 99.5% of the variation and represent\n",
"directional movements, slope movements, and curvature movements respectively.\n",
"Overall, by using principal component analysis, analyzing the eigen vectors and\n",
"understanding the intuition behind them, we demonstrated how the implementation\n",
"of a dimensionality reduction lead to fewer intuitive dimensions in the yield curve.\n"
]
}
],
"metadata": {
"_change_revision": 206,
"_is_fork": false,
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 1
}